Rotational Motion · Physics · MHT CET

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MCQ (Single Correct Answer)

1

A rigid body rotates about a fixed axis with variable angular velocity $(\alpha-\beta t)$ at time $t$, where $\alpha$ and $\beta$ are constants. The angle through which it rotates before it comes to rest is

MHT CET 2025 26th April Morning Shift
2

Moment of inertia of a solid sphere about its diameter is 'I'. It is then casted into 27 small spheres of same diameter. The moment of inertia of each small sphere about its diameter is

MHT CET 2025 26th April Morning Shift
3

Moment of inertia of the rod about an axis passing through the centre and perpendicular to its length is ' $I_1$ '. The same rod is bent into a ring and its moment of inertia about the diameter is ' $I_2$ '. Then $I_1 / I_2$ is

MHT CET 2025 26th April Morning Shift
4

A bob of mass ' $m$ ' is tied by a massless string whose other end is wound on a flywheel (disc) of radius ' $R$ ' and mass ' $m$ '. When released from the rest, the bob starts falling vertically downwards. If the bob has covered a vertical distance ' $h$ ', then angular speed of wheel will be (There is no slipping between string and wheel, g - acceleration due to gravity)

MHT CET 2025 25th April Evening Shift
5

A thin uniform rod of length ' $L$ ' and mass ' $M$ ' is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ' $\omega$ '. Its centre of mass rises to a maximum height of

( $\mathrm{g}=$ acceleration due gravity)

MHT CET 2025 25th April Evening Shift
6

Using Bohr's quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule?

( $I=$ moment of inertia of diatomic molecule and $\mathrm{h}=$ Planck's constant)

MHT CET 2025 25th April Evening Shift
7

The moment of inertia of a solid sphere of mass ' $m$ ' and radius ' $R$ ' about its diametric axis is ' $I$ '. Its moment of inertia about a tangent in the plane is

MHT CET 2025 25th April Evening Shift
8

Two discs of moment of inertia ' $\mathrm{I}_1$ ' and ' $\mathrm{I}_2$ ' and angular speeds ' $\omega_1$ ' and ' $\omega_2$ ' are rotating along the collinear axes passing through their centre of mass and perpendicular to their plane. If the two discs are made to rotate together along the same axis. The rotational kinetic energy of the system will be

MHT CET 2025 25th April Morning Shift
9

Four particles each of mass M are placed at the corners of a square of side L . The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is

MHT CET 2025 25th April Morning Shift
10

What is the linear velocity if angular velocity $\vec{\omega}=3 \hat{i}-4 \hat{j}+\hat{k}$ and radius $\vec{r}=(5 \hat{i}-6 \hat{j}+6 \hat{k})$ ?

MHT CET 2025 23rd April Evening Shift
11

A thin metal wire of length ' L ' and mass ' M ' is bent to form semicircular ring as shown. The moment of inertia about $\mathrm{XX}^{\prime}$ is

MHT CET 2025 22nd April Evening Shift Physics - Rotational Motion Question 12 English
MHT CET 2025 22nd April Evening Shift
12

A solid cylinder of mass ' $M$ ' and radius ' $R$ ' is rotating about its geometrical axis. A solid sphere of same mass and same radius is also rotating about its diameter with an angular speed half that of the cylinder. The ratio of the kinetic energy of rotation of the sphere to that of the cylinder will be

MHT CET 2025 22nd April Evening Shift
13

A solid sphere of mass ' $m$ ' and radius ' $R$ ' is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with angular speed twice that of sphere. The ratio of kinetic energy of sphere to kinetic energy of cylinder will be

MHT CET 2025 22nd April Morning Shift
14

A solid sphere and thin walled hollow sphere have same mass and same material. Which of them have greater moment of inertia about their diameter?

[ $\mathrm{I}_{\mathrm{h}}=$ moment of inertia of hollow sphere about an axis coinciding with its diameter, $\mathrm{I}_5=$ moment of inertia of solid sphere about an axis coinciding with its diameter]

MHT CET 2025 22nd April Morning Shift
15

If force $\vec{F}=-3 \hat{i}+\hat{j}+5 \hat{k}$ acts along $\vec{r}=7 \hat{i}+3 \hat{j}+\hat{k}$ then the torque acting at that point is

MHT CET 2025 22nd April Morning Shift
16

The moment of inertia of a ring about an axis passing through its centre and perpendicular to its plane is I. It is rotating with angular velocity $\omega$. Another identical ring is gently placed on it so that their centres coincide. If both the rings are rotating about the same axis then loss in kinetic energy is

MHT CET 2025 21st April Evening Shift
17

A body is rotating about its own axis. Its rotational kinetic energy is ' x ' and its angular momentum is ' $y$ '. Hence its moment of inertia about its own axis is

MHT CET 2025 21st April Evening Shift
18

Moment of inertia of a thin uniform rod rotating about the perpendicular axis passing through its centre is ' $I$ '. If the same rod is bent in the form of ring, its moment of inertia about the diameter is ' $\mathrm{I}_1$ '. If $\mathrm{I}_1=\mathrm{xI}$, then the value of ' x ' is

MHT CET 2025 21st April Evening Shift
19

A disc of mass 25 kg and radius 0.2 m is rotating at 240 r.p.m. A retarding torque brings it to rest in 20 second. If the torque is due to a force applied tangentially on the rim of the disc then the magnitude of the force is

MHT CET 2025 21st April Morning Shift
20

Two circular loops P and Q of radii ' r ' and ' nr ' are made respectively from a uniform wire. Moment of inertia of loop Q about its axis is 4 times that of loop $P$ about its axis. The value of $n$ is

MHT CET 2025 21st April Morning Shift
21

Three spheres, each of mass ' $m$ ' and radius ' $r$ ' are placed as shown in figure. Consider an axis $\mathrm{YY}^{\prime}$, which is touching two spheres and passing through the diameter of third sphere. The moment of inertia of the system consisting of these three spheres about $\mathrm{YY}^{\prime}$ axis is

MHT CET 2025 21st April Morning Shift Physics - Rotational Motion Question 19 English
MHT CET 2025 21st April Morning Shift
22

A wheel initially at rest, begins to rotate about its axis with constant angular acceleration. If it rotates through an angle $\theta_1$ in first 2 s and a further angle $\theta_2$ in the next 2 s , the ratio $\theta_1: \theta_2$ is

MHT CET 2025 20th April Evening Shift
23

A solid sphere rolling without friction on a horizontal surface with a constant speed of $2 \mathrm{~m} / \mathrm{s}$, rolls up on an inclined ramp which is inclined at $30^{\circ}$. The maximum distance travelled by the sphere on the inclined ramp is (acceleration due to gravity $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2, \sin 30^{\circ}=\frac{1}{2}$ )

MHT CET 2025 20th April Evening Shift
24

A disc of mass ' $m$ ' and radius ' $r$ ' rolls down an inclined plane of height ' $h$ '. When it reaches the bottom of the plane, its rotational kinetic energy is ( $\mathrm{g}=$ acceleration due to gravity)

MHT CET 2025 20th April Evening Shift
25

Two discs A and B of same material and thickness have radii $R$ and $3 R$ respectively. Their moments of inertia about their axis will be in the ratio

MHT CET 2025 20th April Morning Shift
26

An inclined plane makes an angle $30^{\circ}$ with the horizontal. A solid sphere rolling down an inclined plane from rest without slipping has linear acceleration ( $\mathrm{g}=$ acceleration due gravity) ( $\sin 30^{\circ}=0.5$ )

MHT CET 2025 20th April Morning Shift
27

Two spheres each of mass $M$ and radius $R$ are connected with a massless rod of length 4 R . The moment of inertia of the system about an axis passing through the centre of one of the spheres and perpendicular to the rod will be

MHT CET 2025 20th April Morning Shift Physics - Rotational Motion Question 25 English
MHT CET 2025 20th April Morning Shift
28

A body slides down a smooth inclined plane of inclination $\theta$ and reaches the bottom with velocity V . If the same body is a ring which rolls down the same inclined plane then linear velocity at the bottom of plane is

MHT CET 2025 19th April Evening Shift
29
If $\vec{F}=(5 \hat{i}-10 \hat{j})$ and $\vec{r}=(4 \hat{i}-3 \hat{j})$, then the torque acting on the object will be
MHT CET 2025 19th April Morning Shift
30
Four particles each of mass M are placed at the corners of a square of side $L$. The radius of gyration of the system about an axis perpendicular to the square and passing through its centre is
MHT CET 2025 19th April Morning Shift
31

A thin uniform rod of mass ' $m$ ' and length ' $L$ ' is pivoted at one end so that it can rotate in a vertical plane. The free end is held vertically above pivot and then released. The angular acceleration of the rod when it makes an angle ' $\theta$ ' with the vertical is [consider negligible friction at the pivot] ( $\mathrm{g}=$ acceleration due to gravity)

MHT CET 2025 19th April Morning Shift Physics - Rotational Motion Question 28 English

MHT CET 2025 19th April Morning Shift
32
When a ceiling fan is switched off, its angular velocity falls to $\left(\frac{1}{3}\right)^{\text {rd }}$ while it makes 24 rotations. How many more rotations will it make before coming to rest?
MHT CET 2025 19th April Morning Shift
33

Three point masses, each of mass ' $m$ ' are placed at the corners of an equilateral triangle of side ' $L$ '. The moment of inertia of the system about an axis passing through one of the vertices and parallel to the side joining other two vertices will be

MHT CET 2024 16th May Evening Shift
34

Two spheres of equal masses, one of which is a thin spherical shell and the other solid sphere, have the same moment of inertia about their respective diameters. The ratio of their radii is

MHT CET 2024 16th May Morning Shift
35

Two loops P and Q of radii $\mathrm{R}_1$ and $\mathrm{R}_2$ are made from uniform metal wire of same material. $I_p$ and $\mathrm{I}_{\mathrm{Q}}$ be the moment of inertia of loop P and Q respectively then ratio $R_1 / R_2$ is $\left(\right.$ Given $\left.I_P / I_Q=27\right)$

MHT CET 2024 16th May Morning Shift
36

A body of mass $m$ slides down an incline and reaches the bottom with a velocity V . If the same mass were in the form of a disc which rolls down this incline, the velocity of the disc at bottom would have been

MHT CET 2024 15th May Evening Shift
37

The radius of gyration of a circular disc of radius R and mass m rotating about diameter as axis is

MHT CET 2024 15th May Evening Shift
38

A thin uniform metal rod of mass ' $M$ ' and length ' $L$ ' is swinging about a horizontal axis passing through its end. Its maximum angular velocity is ' $\omega$ '. Its centre of mass rises to a maximum height of ( $\mathrm{g}=$ Acceleration due to gravity)

MHT CET 2024 15th May Morning Shift
39

Three thin rods, each of mass ' $M$ ' and length ' $L$ ' are placed along $\mathrm{X}, \mathrm{Y}$ and Z axes which are mutually perpendicular. One end of each rod is at origin. M. I. of the system about Z axis is

MHT CET 2024 15th May Morning Shift
40

If the angular velocity of a body rotating about the given axis increases by $20 \%$, then its kinetic energy of rotation will increase by

MHT CET 2024 15th May Morning Shift
41

Four thin metal rods each of mass ' $M$ ' and length ' $L$ ', are welded end to end to form a square. The moment of inertia of the system about an axis passing through the centre of the square and perpendicular to its plane is

MHT CET 2024 11th May Evening Shift
42

Moment of inertia of a disc about an axis passing through its centre and perpendicular to its plane is 'I'. The ratio of moment of inertia about a parallel axis tangential to its rim to passing through a point midway between the centre and the rim is

MHT CET 2024 11th May Evening Shift
43

An inclined plane makes an angle $30^{\circ}$ with horizontal. A solid sphere rolls down from the top of the inclined plane from rest without slipping has a linear acceleration along the plane equal to (where $g$ is acceleration due to gravity) (given $\sin 30^{\circ}=0.5$)

MHT CET 2024 11th May Morning Shift
44

Two bodies A and B have their moments of inertia $I_1$ and $I_2$ respectively about their axis of rotation. If their kinetic energies of rotation are equal and their angular momenta $\mathrm{L}_1$ and $\mathrm{L}_2$ respectively are in the ratio $1: \sqrt{3}$, then $I_2$ will be

MHT CET 2024 10th May Evening Shift
45

The moment of inertia of uniform circular disc is maximum about an axis perpendicular to the disc and passing through point

MHT CET 2024 10th May Morning Shift Physics - Rotational Motion Question 45 English

MHT CET 2024 10th May Morning Shift
46

A ring and a disc roll on horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is 6 J then total kinetic energy of the disc is

MHT CET 2024 10th May Morning Shift
47

A solid metallic sphere of radius ' $R$ ' having moment of inertia '$I$' about diameter is melted and recast into a solid disc of radius ' $r$ ' of a uniform thickness. The moment of inertia of a disc about an axis passing through its edge and perpendicular to its plane is also equal to '$I$'. The ratio $\frac{r}{R}$ is

MHT CET 2024 10th May Morning Shift
48

A particle of mass ' m ' is rotating in a circular path of radius ' $r$ '. Its angular momentum is ' $L$ ' The centripetal force acting on it is ' $F$ '. The relation between ' $F$ ', ' $L$ ', ' $r$ ' and ' $m$ ' is

MHT CET 2024 9th May Evening Shift
49

Three thin rods, each mass ' 2 M ' and length ' L ' are placed along $\mathrm{x}, \mathrm{y}$ and z axis which are mutually perpendicular. One end of each rod is at origin. Moment of inertia of the system about x - axis is

MHT CET 2024 9th May Evening Shift
50

A thin uniform rod of length ' $L$ ' and mass ' $M$ ' is swinging freely along a horizontal axis passing through its centre. Its maximum angular speed is ' $\omega$ '. Its centre of mass rises to a maximum height of [ $\mathrm{g}=$ gravitational acceleration]

MHT CET 2024 9th May Morning Shift
51

The moment of inertia of thin square plate PQRS of uniform thickness, about an axis passing through centre ' O ' and perpendicular to the plane of the plate is $\left(\mathrm{I}_1, \mathrm{I}_2, \mathrm{I}_3, \mathrm{I}_4\right.$ are respectively the moments of inertia about axis $1,2,3,4$ which are in the plane of the plate as shown in figure)

MHT CET 2024 9th May Morning Shift Physics - Rotational Motion Question 50 English

MHT CET 2024 9th May Morning Shift
52

A circular disc of radius ' $R$ ' and thickness $\frac{R}{8}$ has moment of inertia 'I' about an axis passing through its centre and perpendicular to its plane. It is melted and recasted into a solid sphere then moment of inertia of sphere about an axis passing through diameter is

MHT CET 2024 9th May Morning Shift
53

Two solid spheres ( A and B ) are made of metals having densities $\rho_A$ and $\rho_B$ respectively. If there masses are equal then ratio of their moments of inertia $\left(\frac{\mathrm{I}_{\mathrm{B}}}{\mathrm{I}_{\mathrm{A}}}\right)$ about their respective diameter is

MHT CET 2024 4th May Evening Shift
54

A thin uniform circular disc of mass ' $M$ ' and radius ' $R$ ' is rotating with angular velocity ' $\omega$ ' in a horizontal plane about an axis passing through its centre and perpendicular to its plane. Another disc of same radius but of mass $\left(\frac{\mathrm{M}}{3}\right)$ is placed gently on the first disc co-axially. The new angular velocity will be

MHT CET 2024 4th May Evening Shift
55

A solid cylinder of mass ' $M$ ' and radius ' $R$ ' rolls down an inclined plane of height ' $h$ '. When it reaches the foot of the plane, its rotational kinetic energy is ( $\mathrm{g}=$ acceleration due to gravity)

MHT CET 2024 4th May Evening Shift
56

A disc and a ring both have same mass and radius. The ratio of moment of inertia of the disc about its diameter to that of a ring about a tangent in its plane is

MHT CET 2024 4th May Morning Shift
57

A rotating body has angular momentum ' $L$ '. If its frequency is doubled and kinetic energy is halved, its angular momentum will be

MHT CET 2024 4th May Morning Shift
58

A solid cylinder of mass M and radius R is rotating about its geometrical axis. A solid sphere of the same mass and same radius is also rotating about its diameter with an angular speed half that of the cylinder. The ratio of the kinetic energy of rotation of the sphere to that of the cylinder will be

MHT CET 2024 4th May Morning Shift
59

The earth is assumed to be a sphere of radius ' $R$ ' and mass ' $M$ ' having period of rotation ' $T$ '. The angular momentum of earth about its axis of rotation is

MHT CET 2024 3rd May Evening Shift
60

Two loops ' $A$ ' and ' $B$ ' of radii ' $R_1$ ' and ' $R_2$ ' are made from uniform wire. If moment of inertia of ' A ' is ' $\mathrm{I}_{\mathrm{A}}$ ' and that ' B ' is ' $\mathrm{I}_{\mathrm{B}}$ ', then $\mathrm{R}_2 / \mathrm{R}_1$ is $\left[\frac{\mathrm{I}_{\mathrm{A}}}{\mathrm{I}_{\mathrm{B}}}=27\right]$

MHT CET 2024 3rd May Evening Shift
61

In case of rotational dynamics, which one of the following statements is correct?

[$\vec{\omega}=$ angular velocity, $\overrightarrow{\mathrm{v}}=$ linear velocity

$\overrightarrow{\mathbf{r}}=$ radius vector, $\vec{\alpha}=$ angular acceleration

$\overrightarrow{\mathrm{a}}=$ linear acceleration, $\overrightarrow{\mathrm{L}}=$ angular momentum

$\overrightarrow{\mathrm{p}}=$ linear momentum, $\bar{\tau}=$ torque,

$\overrightarrow{\mathrm{f}}=$ centripetal force]

MHT CET 2024 3rd May Morning Shift
62

Ratio of radius of gyration of a circular disc to that of circular ring each of same mass and radius around their respective axes is

MHT CET 2024 3rd May Morning Shift
63

Two circular loops P and Q of radii ' r ' and ' nr ' are made respectively from a uniform wire. Moment of inertia of loop Q about its axis is four times that of loop P about its axis. The value of ' $n$ ' is

MHT CET 2024 3rd May Morning Shift
64

A solid sphere of mass ' $m$ ', radius ' $R$ ', having moment of inertia about an axis passing through center of mass as 'I' is recast into a disc of thickness ' $t$ ' whose moment of inertia about an axis passing through the rim (edge) \& perpendicular to plane remains 'I'. Then the radius of disc is

MHT CET 2024 2nd May Evening Shift
65

An inclined plane makes an angle of $30^{\circ}$ with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration ( $\mathrm{g}=$ acceleration due to gravity, $\sin 30^{\circ}=0.5$ )

MHT CET 2024 2nd May Evening Shift
66

An annular ring has mass 10 kg and inner and outer radii are 10 m and 5 m respectively. Its moment of inertia about an axis passing through its centre and perpendicular to its plane is

MHT CET 2024 2nd May Morning Shift
67

Four identical uniform solid spheres each of same mass '$$M$$' and radius '$$R$$' are placed touching each other as shown in figure, with centres A, B, C, D. $$\mathrm{I}_{\mathrm{A}}, \mathrm{I}_{\mathrm{B}}, \mathrm{I}_{\mathrm{C}}$$ and $$\mathrm{I}_{\mathrm{D}}$$ are the moment of inertia of these spheres respectively about an axis passing through centre and perpendicular to the plane. The difference in $$\mathrm{I}_{\mathrm{A}}$$, and $$\mathrm{I}_{\mathrm{B}}$$ is

MHT CET 2023 14th May Evening Shift Physics - Rotational Motion Question 101 English

MHT CET 2023 14th May Evening Shift
68

A solid cylinder and a solid sphere having same mass and same radius roll down on the same inclined plane. The ratio of the acceleration of the cylinder '$$a_c$$' to that of sphere '$$a_s$$' is

MHT CET 2023 14th May Evening Shift
69

A mass '$$M$$' is moving with constant velocity parallel to $$\mathrm{X}$$-axis. Its angular momentum with respect to the origin is

MHT CET 2023 14th May Evening Shift
70

A thin uniform rod of mass '$$m$$' and length '$$P$$' is suspended from one end which can oscillate in a vertical plane about the point of intersection. It is pulled to one side and then released. It passes through the equilibrium position with angular speed '$$\omega$$'. The kinetic energy while passing through mean position is

MHT CET 2023 14th May Morning Shift
71

Four identical uniform solid spheres each of same mass $$M$$ and radius $$R$$ are placed touching each other as shown in figure with centres $$A, B, C, D. I_A, I_B, I_C, I_D$$ are the moment of inertia of these spheres respectively about an axis passing through centre and perpendicular to the plane, then

MHT CET 2023 13th May Evening Shift Physics - Rotational Motion Question 102 English

MHT CET 2023 13th May Evening Shift
72

A thin uniform $$\operatorname{rod} A B$$ of mass $$m$$ and length $$l$$ is hinged at one end $$A$$ to the ground level. Initially the rod stands vertically and is allowed to fall freely to the ground in the vertical plane. The angular velocity of the rod when its end $$B$$ strikes the ground is ( $$g=$$ acceleration due to gravity)

MHT CET 2023 13th May Evening Shift
73

A rigid body rotates with an angular momentum L. If its rotational kinetic energy is made four times, its angular momentum will become

MHT CET 2023 13th May Morning Shift
74

The rotational kinetic energy and translational kinetic energy of a rolling body are same, the body is

MHT CET 2023 13th May Morning Shift
75

A solid cylinder of mass $$3 \mathrm{~kg}$$ is rolling on a horizontal surface with velocity $$4 \mathrm{~m} / \mathrm{s}$$. It collides with a horizontal spring whose one end is fixed to rigid support. The force constant of material of spring is $$200 \mathrm{~N} / \mathrm{m}$$. The maximum compression produced in the spring will be (assume collision between cylinder & spring be elastic)

MHT CET 2023 13th May Morning Shift
76

A thin wire of length '$$L$$' and uniform linear mass density '$$m$$' is bent into a circular coil. The moment of inertia of this coil about tangential axis and in plane of the coil is

MHT CET 2023 12th May Evening Shift
77

In $$\mathrm{P}^{\text {th }}$$ second, a particle describes angular displacement of '$$\beta$$' rad. If it starts from rest, the angular acceleration is

MHT CET 2023 12th May Evening Shift
78

$$I_1$$ is the moment of inertia of a circular disc about an axis passing through its centre and perpendicular to the plane of disc. $$I_2$$ is its moment of inertia about an axis $$A B$$ perpendicular to plane and parallel to axis $$\mathrm{CM}$$ at a distance $$\frac{2 R}{3}$$ from centre. The ratio of $$I_1$$ and $$I_2$$ is $$x: 17$$. The value of '$$x$$' is (R = radius of the disc)

MHT CET 2023 12th May Morning Shift Physics - Rotational Motion Question 108 English

MHT CET 2023 12th May Morning Shift
79

A thin uniform circular disc of mass '$$\mathrm{M}$$' and radius '$$R$$' is rotating with angular velocity '$$\omega$$', in a horizontal plane about an axis passing through its centre and perpendicular to its plane. Another disc of same radius but of mass $$\left(\frac{M}{2}\right)$$ is placed gently on the first disc co-axially. The new angular velocity will be

MHT CET 2023 12th May Morning Shift
80

Two bodies have their moments of inertia I and 2I respectively about their axis of rotation. If their kinetic energies of rotation are equal, their angular momenta will be in the ratio

MHT CET 2023 11th May Evening Shift
81

From a disc of mass '$$M$$' and radius '$$R$$', a circular hole of diameter '$$R$$' is cut whose rim passes through the centre. The moment of inertia of the remaining part of the disc about perpendicular axis passing through the centre is

MHT CET 2023 11th May Evening Shift
82

A particle moves along a circular path with decreasing speed. Hence

MHT CET 2023 11th May Morning Shift
83

Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is $$\mathrm{K}_{\mathrm{c}}$$. Radius of gyration of the same disc about a diameter of the disc is $$K_d$$. The ratio $$K_c: K_d$$ is

MHT CET 2023 11th May Morning Shift
84

A disc has mass $$M$$ and radius $$R$$. How much tangential force should be applied to the rim of the disc, so as to rotate with angular velocity '$$\omega$$' in time $$\mathrm{t}$$ ?

MHT CET 2023 11th May Morning Shift
85

What is the moment of inertia of the electron moving in second Bohr orbit of hydrogen atom? [ $$\mathrm{h}=$$ Planck's constant, $$\mathrm{m}=$$ mass of electron, $$\varepsilon_0=$$ permittivity of free space, $$\mathrm{e}=$$ charge on electron]

MHT CET 2023 10th May Evening Shift
86

Two spheres each of mass '$$M$$' and radius $$\frac{R}{2}$$ are connected at the ends of massless rod of length '$$2 R$$'. What will be the moment of inertia of the system about an axis passing through centre of one of the spheres and perpendicular to the rod?

MHT CET 2023 10th May Evening Shift
87

The moment of inertia of a uniform square plate about an axis perpendicular to its plane and passing through the centre is $$\frac{\mathrm{Ma}^2}{6}$$, where '$$M$$' is the mass and '$$a$$' is the side of square plate. Moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

MHT CET 2023 10th May Evening Shift
88

If 'I' is moment of inertia of a thin circular disc about an axis passing through the tangent of the disc and in the plane of disc. The moment of inertia of same circular disc about an axis perpendicular to plane and passing through its centre is

MHT CET 2023 10th May Morning Shift
89

Seven identical discs each of mass $$M$$ and radius $$\mathrm{R}$$ are arranged in a hexagonal plane pattern so as to touch each neighbour disc as shown in the figure. The moment of inertia of the system of seven discs about an axis passing through the centre of central disc and normal to the plane of all discs is

MHT CET 2023 10th May Morning Shift Physics - Rotational Motion Question 111 English

MHT CET 2023 10th May Morning Shift
90

A particle of mass '$$\mathrm{m}$$' is rotating along a circular path of radius '$$r$$' having angular momentum '$$L$$'. The centripetal force acting on the particle is given by

MHT CET 2023 10th May Morning Shift
91

A disc of radius $$R$$ and thickness $$\frac{R}{6}$$ has moment of inertia I about an axis passing through its centre and perpendicular to its plane. Dise is melted and recast into a solid sphere. The moment of inertia of a sphere about its diameter is

MHT CET 2023 9th May Evening Shift
92

A square lamina of side '$$b$$' has same mass as a disc of radius '$$R$$' the moment of inertia of the two objects about an axis perpendicular to the plane and passing through the centre is equal. The ratio $$\frac{b}{R}$$ is

MHT CET 2023 9th May Morning Shift
93

A solid sphere rolls without slipping on an inclined plane at an angle $$\theta$$. The ratio of total kinetic energy to its rotational kinetic energy is

MHT CET 2023 9th May Morning Shift
94

Two discs of same mass and same thickness (t) are made from two different materials of densities '$$d_1$$' and '$$d_2$$' respectively. The ratio of the moment of inertia $$I_1$$ to $$I_2$$ of two discs about an axis passing through the centre and perpendicular to the plane of disc is

MHT CET 2023 9th May Morning Shift
95

The moment of inertia of a thin uniform rod of mass 'M' and length 'L' about an axis passing through a point at a distance $$\frac{L}{4}$$ from one of its ends and perpendicular to the length of the rod is

MHT CET 2021 24th September Evening Shift
96

Two identical particles each of mass '$$m$$' are separated by a distance '$$d$$'. The axis of rotation passes through the midpoint of '$$\mathrm{d}$$' and is perpendicular to the length $$\mathrm{d}$$. If '$$\mathrm{K}$$' is the average rotational kinetic energy of the system, then the angular frequency is

MHT CET 2021 24th September Morning Shift
97

A body of mass '$$\mathrm{m}$$' and radius of gyration '$$\mathrm{K}$$' has an angular momentum $$\mathrm{L}$$. Its angular velocity is

MHT CET 2021 24th September Morning Shift
98

The moment of inertia of a body about the given axis, rotating with angular velocity 1 rad/s is numerically equal to 'P' times its rotational kinetic energy. The value of 'P' is

MHT CET 2021 23rd September Evening Shift
99

Two circular loops P and Q are made from a uniform wire. The radii of P and Q are R$$_1$$ and R$$_2$$ respectively. The momentsw of inertia about their own axis are $$\mathrm{I_P}$$ and $$\mathrm{I_Q}$$ respectively. If $$ \frac{\mathrm{I}_{\mathrm{P}}}{\mathrm{I}_Q}=\frac{1}{8}$$ then $$\mathrm{\frac{R_2}{R_1}}$$ is

MHT CET 2021 23rd September Evening Shift
100

A metre scale is supported on a wedge at its centre of gravity. A body of weight 'w'. is suspended from the $$20 \mathrm{~cm}$$ mark and another weight of 25 gram is suspended from $$74 \mathrm{~cm}$$ mark balance it and the metre scale remains perfectly horizontal. Neglecting the weight of the metre scale, the weight of the body is

MHT CET 2021 23rd September Evening Shift
101

A body of mass 'm' and radius of gyration 'K' has an angular momentum 'L'. Then its angular velocity is

MHT CET 2021 23rd September Evening Shift
102

A molecule consists of two atoms each of mass '$$m$$' and separated by a distance '$$\mathrm{d}$$'. At room temperature, if the average rotational kinetic energy is '$$E$$' then the angular frequency is

MHT CET 2021 23th September Morning Shift
103

Three solid spheres each of mass '$$M$$' and radius '$$R$$' are arranged as shown in the figure. The moment of inertia of the system about YY' will be

MHT CET 2021 23th September Morning Shift Physics - Rotational Motion Question 90 English

MHT CET 2021 23th September Morning Shift
104

MHT CET 2021 23th September Morning Shift Physics - Rotational Motion Question 91 English

Figure shows triangular lamina which can rotate about different axes moment of inertia is maximum, about the axis

MHT CET 2021 23th September Morning Shift
105

A particle with position vector $$\overrightarrow{\mathrm{r}}$$ has a linear momentum $$\overrightarrow{\mathrm{P}}$$. Which one of the following statements is true in respect of its angular momentum 'L' about the origin?

MHT CET 2021 22th September Evening Shift
106

A child is standing with folded hands at the centre of the platform rotating about its central axis. The kinetic energy of the system is '$$K$$'. The child now stretches his arms so that the moment of inertia of the system becomes double. The kinetic energy of the system now is

MHT CET 2021 22th September Evening Shift
107

Two rings of radius 'R' and 'nR' made of same material have the ratio of moment of inertia about an axis passing through its centre and perpendicular to the plane is $$1: 8$$. The value of '$$n$$' is (mass per unit length $$=\lambda$$)

MHT CET 2021 22th September Evening Shift
108

Two rotating bodies $$P$$ and $$Q$$ of masses '$$\mathrm{m}$$' and '$$2 \mathrm{~m}$$' with moment of inertia $$I_P$$ and $$I_Q\left(I_Q > I_P\right)$$ have equal Kinetic energy of rotation. If $$\mathrm{L}_P$$ and $$\mathrm{L}_Q$$ be their angular momenta respectively then

MHT CET 2021 22th September Morning Shift
109

A solid sphere of mass '$$M$$' and radius '$$R$$' is rotating about its diameter. A solid cylinder of same mass and same radius is also rotating about its geometrical axis with an angular speet twice that of the sphere. The ratio of the kinetic energy of rotation of the sphere to that of the cylinder is

MHT CET 2021 22th September Morning Shift
110

A particle performs rotational motion with an angular momentum 'L'. If frequency of rotation is doubled and its kinetic energy becomes one fourth, the angular momentum becomes.

MHT CET 2021 21th September Evening Shift
111

MHT CET 2021 21th September Evening Shift Physics - Rotational Motion Question 128 English

Three rings each of mass 'M' and radius 'R' are arranged as shown in the figure. The moment of inertia of system about axis YY' will be

MHT CET 2021 21th September Evening Shift
112

The moment of inertia of a circular disc of radius $$2 \mathrm{~m}$$ and mass $$1 \mathrm{~kg}$$ about an axis XY passing through its centre of mass and perpendicular to the plane of the disc is $$2 \mathrm{~kg} \mathrm{~m}^2$$. The moment of inertia about an axis parallel to the axis $$\mathrm{XY}$$ and passing through the edge of the disc is

MHT CET 2021 21th September Morning Shift
113

The moment of inertia of a body about a given axis is $$1.2 \mathrm{~kg} / \mathrm{m}^3$$. Initially the body is at rest. In order to produce rotational kinetic energy of $$1500 \mathrm{~J}$$, an angular acceleration of $$25 \mathrm{rad} / \mathrm{s}^2$$ must be applied about an axis for a time duration of

MHT CET 2021 21th September Morning Shift
114

A disc of radius 0.4 metre and mass 1 kg rotates about an axis passing through its centre and perpendicular to its plane. The angular acceleration is 10 rad s$$^{-2}$$. The tangential force applied to the rim of the disc is

MHT CET 2021 20th September Evening Shift
115

The ratio of radii of gyration of a circular ring and circular disc of the same mass and radius, about an axis passing through their centres and perpendicular to their planes is

MHT CET 2021 20th September Evening Shift
116

A solid sphere of mass $$\mathrm{M}$$, radius $$\mathrm{R}$$ has moment of inertia '$$\mathrm{I}$$' about its diameter. It is recast into a disc of thickness 't' whose moment of inertia about an axis passing through its edge and perpendicular to its plane remains 'I'. Radius of the disc will be

MHT CET 2021 20th September Morning Shift
117

Two bodies rotate with kinetic energies 'E$$_1$$' and 'E$$_2$$'. Moments of inertia about their axis of rotation are 'I$$_1$$' and 'I$$_2$$'. If $$\mathrm{I_1=\frac{I_2}{3}}$$ and E$$_1$$ = 27 E$$_2$$, then the ratio of angular momenta 'L$$_1$$' to 'L$$_2$$' is

MHT CET 2021 20th September Morning Shift
118

A disc of radius 0.4 m and mass one kg rotates about an axis passing through its centre and perpendicular to its plane. The angular acceleration of the disc is 10 rad/s$$^2$$. The tangential force applied to the rim of the disc is

MHT CET 2021 20th September Morning Shift
119

Three points masses, each of mass $m$ are placed at the corners of an equilateral triangle of side $\ell$. The moment of inertia of the system about an axis passing through one of the vertices and parallel to the side joining other two vertices, will be

MHT CET 2020 19th October Evening Shift
120

A rope is wound around a solid cylinder of mass 1 kg and radius 0.4 m . What is the angular acceleration of cylinder, if the rope is pulled with a force of 25 N ? (Cylinder is rotating about its own axis.)

MHT CET 2020 19th October Evening Shift
121

Two circular loop $A$ and $B$ of radii $R$ and $N R$ respectively are made from a uniform wire. Moment of inertia of $B$ about its axis is 3 times that of $A$ about its axis. The value of $N$ is

MHT CET 2020 19th October Evening Shift
122

A body slides down a smooth inclined plane having angle $$\theta$$ and reaches the bottom with velocity $$v$$. If a body is a sphere, then its linear velocity at the bottom of the plane is

MHT CET 2020 16th October Evening Shift
123

A thin uniform rod has mass $$M$$ and length $$L$$ The moment of inertia about an axis perpendicular to it and passing through the point at a distance $$\frac{L}{3}$$ from one of its ends, will be

MHT CET 2020 16th October Evening Shift
124

The ratio of radii of gyration of a ring to a disc (both circular) of same radii and mass, about a tangential axis perpendicular to the plane is

MHT CET 2020 16th October Evening Shift
125

If there is a change of angular momentum from $$1 \mathrm{j}$$-$$\mathrm{s}$$ to $$4 \mathrm{j}$$-$$\mathrm{s}$$ in $$4 \mathrm{~s}$$, then the torque

MHT CET 2020 16th October Morning Shift
126

A solid cylinder of radius $$r$$ and mass $$M$$ rolls down an inclined plane of height $$h$$. When it reaches the bottom of the plane, then its rotational kinetic energy is ($$g=$$ acceleration due to gravity)

MHT CET 2020 16th October Morning Shift
127

A rod $l \mathrm{~m}$ long is acted upon by a couple as shown in the figure. The moment of couple is $\tau \mathrm{~Nm}$. If the force at each end of the rod, then magnitude of each force is

$$\left(\sin 30^{\circ}=\cos 60^{\circ}=0.5\right)$$

MHT CET 2019 3rd May Morning Shift Physics - Rotational Motion Question 69 English

MHT CET 2019 3rd May Morning Shift
128

A solid sphere rolls down from top of inclined plane, 7 m high, without slipping. Its linear speed at the foot of plane is $\left(g=10 \mathrm{~m} / \mathrm{s}^2\right)$

MHT CET 2019 3rd May Morning Shift
129

Three identical rods each of mass ' $M$ ' and length ' $L$ ' are joined to form a symbol ' $H$. The moment of inertia of the system about one of the sides of ' $H$ ' is

MHT CET 2019 2nd May Evening Shift
130

Three point masses each of mass ' $m$ ' are kept at the corners of an equilateral triangle of side. The system rotates about the center of the triangle without any change in the separation of masses during rotation. The period of rotation is directly proportional to $\left(\cos 30^{\circ}=\sin 60^{\circ}=\frac{\sqrt{3}}{2}\right)$

MHT CET 2019 2nd May Evening Shift
131

When a 12000 joule of work is done on a flywheel, its frequency of rotation increases from 10 Hz to 20 Hz . The moment of inertia of flywheel about its axis of rotation is $\left(\pi^2=10\right)$

MHT CET 2019 2nd May Evening Shift
132

A rigid body is rotating with angular velocity ' $\omega$ ' about an axis of rotation. Let $v$ ' be the linear velocity of particle which is at perpendicular distance ' $r$ ' from the axis of rotation. Then the relation $v=r \omega$ ' implies that

MHT CET 2019 2nd May Evening Shift
133

If radius of the solid sphere is doubled by keeping its mass constant, the ratio of their moment of inertia about any of its diameter is

MHT CET 2019 2nd May Morning Shift
134

A uniform rod of length ' 6 L ' and mass ' 8 m ' is pivoted at its centre ' $C$ '. Two masses ' $m$ ' and ' $2 m^{\prime}$ with speed $2 v, v$ as shown strikes the rod and stick to the rod. Initially the rod is at rest. Due to impact, if it rotates with angular velocity ' $\omega$ ' then ' $\omega$ ' will be

MHT CET 2019 2nd May Morning Shift Physics - Rotational Motion Question 74 English

MHT CET 2019 2nd May Morning Shift
135

A thin metal wire of length 'L' and uniform linear mass density '$\rho$' is bent into a circular coil with 'O' as centre. the moment of inertia of a coil about the axis XX' is

MHT CET 2019 2nd May Morning Shift Physics - Rotational Motion Question 73 English

MHT CET 2019 2nd May Morning Shift
136

The dimensions of torque are same as that of

MHT CET 2019 2nd May Morning Shift
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