## Numerical

Moment of inertia of a disc of mass '$$M$$' and radius '$$R$$' about any of its diameter is $$\frac{M R^{2}}{4}$$. The moment of inertia of this disc ...

A solid cylinder is released from rest from the top of an inclined plane of inclination $$30^{\circ}$$ and length $$60 \mathrm{~cm}$$. If the cylinder...

Two discs of same mass and different radii are made of different materials such that their
thicknesses are $1 \mathrm{~cm}$ and $0.5 \mathrm{~cm}$ re...

A uniform disc of mass $0.5 \mathrm{~kg}$ and radius $r$ is projected with velocity $18 \mathrm{~m} / \mathrm{s}$ at $\mathrm{t}=0$ s on a rough horiz...

A thin uniform rod of length $$2 \mathrm{~m}$$, cross sectional area '$$A$$' and density '$$\mathrm{d}$$' is rotated about an axis passing through the...

A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J. The velocity of centre of mass of the sphere wi...

If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its pl...

$$\mathrm{I_{CM}}$$ is the moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. ...

A uniform solid cylinder with radius R and length L has moment of inertia I$$_1$$, about the axis of the cylinder. A concentric solid cylinder of radi...

Solid sphere A is rotating about an axis PQ. If the radius of the sphere is 5 cm then its radius of gyration about PQ will be $$\sqrt x$$ cm. The valu...

Four identical discs each of mass '$$\mathrm{M}$$' and diameter '$$\mathrm{a}$$' are arranged in a small plane as shown in figure. If the moment of in...

A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, ...

A pulley of radius $$1.5 \mathrm{~m}$$ is rotated about its axis by a force $$F=\left(12 \mathrm{t}-3 \mathrm{t}^{2}\right) N$$ applied tangentially (...

The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be ___________ $...

A disc of mass $$1 \mathrm{~kg}$$ and radius $$\mathrm{R}$$ is free to rotate about a horizontal axis passing through its centre and perpendicular to ...

Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 3 m each. Takin...

Four particles with a mass of 1 kg, 2 kg, 3 kg and 4 kg are situated at the corners of a square with side 1 m (as shown in the figure). The moment of ...

The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I1. The same rod is bent into a ring and its moment ...

A uniform disc with mass M = 4 kg and radius R = 10 cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m = 2 kg hangs from...

Moment of Inertia (M.I.) of four bodies having same mass 'M' and radius '2R' are as follows:
I1 = M.I. of solid sphere about its diameter
I2 = M.I. of...

A 2 kg steel rod of length 0.6 m is clamped on a table vertically at its lower end and is free to rotate in vertical plane. The upper end is pushed so...

In the given figure, two wheels P and Q are connected by a belt B. The radius of P is three times as that of Q. In case of same rotational kinetic ene...

A solid disc of radius 20 cm and mass 10 kg is rotating with an angular velocity of 600 rpm, about an axis normal to its circular plane and passing th...

A particle of mass 'm' is moving in time 't' on a trajectory given by$$\overrightarrow r = 10\alpha {t^2}\widehat i + 5\beta (t - 5)\widehat j$$Where...

The centre of a wheel rolling on a plane surface moves with a speed v0. A particle on the rim of the wheel at the same level as the centre will be mov...

Two bodies, a ring and a solid cylinder of same material are rolling down without slipping an inclined plane. The radii of the bodies are same. The ra...

A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 sec. The number of rotations made in the process is ______...

A circular disc reaches from top to bottom of an inclined plane of length 'L'. When it slips down the plane, it makes time 't1'. When it rolls down th...

The angular speed of truck wheel is increased from 900 rpm to 2460 rpm in 26 seconds. The number of revolutions by the truck engine during this time i...

The following bodies,(1) a ring(2) a disc(3) a solid cylinder(4) a solid sphere,of same mass 'm' and radius 'R' are allowed to roll down without slipp...

A solid disc of radius 'a' and mass 'm' rolls down without slipping on an inclined plane making an angle $$\theta$$ with the horizontal. The accelerat...

Consider a 20 kg uniform circular disk of radius 0.2 m. It is pin supported at its center and is at rest initially. The disk is acted upon by a consta...

Consider a frame that is made up of two thin massless rods AB and AC as shown in the figure. A vertical force $$\overrightarrow P $$ of magnitude 100 ...

A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string are i...

A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the c...

The centre of mass of solid hemisphere of radius 8 cm is x from the centre of the flat surface. Then
value of x is __________.

A force $$\overrightarrow F = \left( {\widehat i + 2\widehat j + 3\widehat k} \right)$$ N acts at a point $$\left( {4\widehat i + 3\widehat j - \wide...

A circular disc of mass M and radius R is rotating about its axis with angular speed $${\omega _1}$$
. If another
stationary disc having radius $${R \...

An massless equilateral triangle EFG of side ‘a’ (As shown in figure) has three particles of mass m
situated at its vertices. The moment of inertia of...

A person of 80 kg mass is standing on the rim
of a circular platform of mass 200 kg rotating
about its axis at 5 revolutions per minute (rpm).
The per...

A square shaped hole of side l = $${a \over 2}$$ is carved
out at a distance d = $${a \over 2}$$ from the centre ‘O’ of
a uniform circular disk of rad...

One end of a straight uniform 1m long bar is
pivoted on horizontal table. It is released from
rest when it makes an angle 30º from the
horizontal (see...

A body of mass m = 10 kg is attached to one
end of a wire of length 0.3 m. The maximum
angular speed (in rad s–1) with which it can be
rotated about i...

Consider a uniform cubical box of side a on a rough floor that is to be moved by applying
minimum possible force F at a point b above its centre of m...

## MCQ (Single Correct Answer)

A solid cylinder and a solid sphere, having same mass $$M$$ and radius $$R$$, roll down the same inclined plane from top without slipping. They start ...

A spherical shell of 1 kg mass and radius R is rolling with angular speed $$\omega$$ on horizontal plane (as shown in figure). The magnitude of angula...

A ball is spun with angular acceleration $$\alpha$$ = 6t2 $$-$$ 2t where t is in second and $$\alpha$$ is in rads$$-$$2. At t = 0, the ball has angula...

A $$\sqrt {34} $$ m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure....

Match List-I with List-II
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;border-style:solid;border-width:1px;font-family...

When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with th...

One end of a massless spring of spring constant k and natural length l0 is fixed while the other end is connected to a small object of mass m lying on...

A solid spherical ball is rolling on a frictionless horizontal plane surface about its axis of symmetry. The ratio of rotational kinetic energy of the...

A thin circular ring of mass M and radius R is rotating with a constant angular velocity 2 rads$$-$$1 in a horizontal plane about an axis vertical to ...

A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendi...

A system consists of two identical spheres each of mass 1.5 kg and radius 50 cm at the end of light rod. The distance between the centres of the two s...

Two discs have moments of inertia I1 and I2 about their respective axes perpendicular to the plane and passing through the centre. They are rotating w...

A huge circular arc of length 4.4 ly subtends an angle '4s' at the centre of the circle. How long it would take for a body to complete 4 revolution if...

The solid cylinder of length 80 cm and mass M has a radius of 20 cm. Calculate the density of the material used if the moment of inertia of the cylind...

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Moment of inertia of a circular d...

Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they star...

A body rolls down an inclined plane without slipping. The kinetic energy of rotation is 50% of its translational kinetic energy. The body is :

A particle of mass m moves in a circular orbit under the central potential field, $$U(r) = - {C \over r}$$, where C is a positive constant. The corre...

Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wir...

A solid cylinder of mass m is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictiona...

A thin circular ring of mass M and radius r is rotating about its axis with an angular speed $$\omega$$. Two particles having mass m each are now atta...

A sphere of mass 2 kg and radius 0.5 m is rolling with an initial speed of 1 ms-1 goes up an inclined plane which makes an angle of 30$$^\circ$$ with ...

A mass M hangs on a massless rod of length l which rotates at a constant angular frequency. The mass M moves with steady speed in a circular path of c...

A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm. If the block takes 40 s to...

The maximum and minimum distances of a comet from the Sun are 1.6 $$\times$$ 1012 m and 8.0 $$\times$$ 1010 m respectively. If the speed of the comet ...

A cord is wound round the circumference of wheel of radius r. The axis of the wheel is horizontal and the moment of inertia about it is I. A weight mg...

Four identical solid spheres each of mass 'm' and radius 'a' are placed with their centres on the four corners of a square of side 'b'. The moment of ...

A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inve...

A sphere of radius 'a' and mass 'm' rolls along a horizontal plane with constant speed v0. It encounters an inclined plane at angle $$\theta$$ and cli...

A circular hole of radius $$\left( {{a \over 2}} \right)$$ is cut out of a circular disc of radius 'a' as shown in figure. The centroid of the remaini...

Moment of inertia (M. I.) of four bodies, having same mass and radius, are reported as; I1 = M.I. of thin circular ring about its diameter,I2 = M.I. o...

The linear mass density of a thin rod AB of length L varies from A to B as
$$\lambda \left( x \right) = {\lambda _0}\left( {1 + {x \over L}} \right)$$...

Four point masses, each of mass m, are fixed at the corners of a square of side $$l$$. The square is
rotating with angular frequency $$\omega $$, abou...

Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is M, radius of its
top, R and height, H, then its moment of inerti...

A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite
when it is farthest from the planet is 6 ti...

A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the
tip of the hand (in units of ms–2) is of the order of...

A ring is hung on a nail. It can oscillate, without
slipping or sliding (i) in its plane with a time
period T1 and, (ii) back and forth in a direction...

A wheel is rotating freely with an angular speed
$$\omega $$ on a shaft. The moment of inertia of the
wheel is I and the moment of inertia of the
shaf...

Consider two uniform discs of the same thickness and different radii R1
= R and R2
= $$\alpha $$R made of
the same material. If the ratio of their m...

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes
perpendicular to the sheet and passing through O (...

A uniform rod of length ‘$$l$$’ is pivoted at one of its ends on a vertical shaft of negligible radius.
When the shaft rotates at angular speed $$\ome...

Moment of inertia of a cylinder of mass M,
length L and radius R about an axis passing
through its centre and perpendicular to the
axis of the cylinde...

Two uniform circular discs are rotating
independently in the same direction around
their common axis passing through their
centres. The moment of iner...

A bead of mass m stays at point P(a, b) on a
wire bent in the shape of a parabola y = 4Cx2
and rotating with angular speed $$\omega $$ (see figure).
T...

Shown in the figure is rigid and uniform one
meter long rod AB held in horizontal position by
two strings tied to its ends and attached to the
ceilin...

A uniform cylinder of mass M and radius R is to
be pulled over a step of height a (a < R) by
applying a force F at its centre ‘O’
perpendicular to ...

A spring mass system (mass m, spring
constant k and natural length $$l$$) rest in
equilibrium on a horizontal disc. The free end
of the spring is fixe...

A rod of length L has non-uniform linear mass
density given by $$\rho $$(x) = $$a + b{\left( {{x \over L}} \right)^2}$$
, where a
and b are constants ...

A uniformly thick wheel with moment of inertia
I and radius R is free to rotate about its centre
of mass (see fig). A massless string is wrapped
over ...

Three solid spheres each of mass m and
diameter d are stuck together such that the lines
connecting the centres form an equilateral
triangle of side ...

As shown in figure, when a spherical cavity
(centered at O) of radius 1 is cut out of a uniform
sphere of radius R (centered at C), the centre of
mass...

A uniform sphere of mass 500 g rolls without
slipping on a plane horizontal surface with its
centre moving at a speed of 5.00 cm/s. Its
kinetic energy...

Consider a uniform rod of mass M = 4m and
length $$\ell $$ pivoted about its centre. A mass m
moving with velocity v making angle $$\theta = {\pi \o...

The coordinates of centre of mass of a uniform
flag shaped lamina (thin flat plate) of mass 4kg.
(The coordinates of the same are shown in
figure) are...

A particle of mass m is fixed to one end of a
light spring having force constant k and
unstretched length $$\ell $$. The other end is fixed. The
syste...

Mass per unit area of a circular disc of radius $$a$$ depends on the distance r from its centre as $$\sigma \left( r \right)$$ = A + Br
. The moment o...

The radius of gyration of a uniform rod of length $$l$$, about an axis passing through a
point $${l \over 4}$$ away from the centre of the rod,
and pe...

Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as ...

A smooth wire of length 2$$\pi $$r is bent into a circle and kept in a vertical plane. A bead can slide smoothly on
the wire. When the circle is rotat...

A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc
varies as $$\left( {{{{\sigma _0}...

A uniform rod of length $$\ell $$ is being rotated in a horizontal plane with a constant angular speed about an axis
passing through one of its ends. ...

A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude $$\theta $$0. If the
person stands up when the swing pass...

A metal coin of mass 5 g and radius 1 cm is fixed to a thin stick AB of negligible mass as shown in the
figure. The system is initially at rest. The c...

Two coaxial discs, having moments of inertia
I1 and I1/2, are rotating with respective angular
velocities $$\omega $$1 and
$$\omega $$1/2
, about the...

Moment of inertia of a body about a given axis
is 1.5 kg m2. Initially the body is at rest. In order
to produce a rotational kinetic energy of
1200 J,...

A thin smooth rod of length L and mass M is
rotating freely with angular speed $$\omega $$0 about an
axis perpendicular to the rod and passing
through...

A stationary horizontal disc is free to rotate
about its axis. When a torque is applied on it,
its kinetic energy as a function of $$\theta $$, where ...

An electric dipole is formed by two equal and
opposite charges q with separation d. The
charges have same mass m. It is kept in a
uniform electric fie...

A rectangular solid box of length 0.3 m is held
horizontally, with one of its sides on the edge
of a platform of height 5m. When released, it
slips of...

Four particles A, B, C and D with masses
mA = m, mB = 2m, mC = 3m and mD = 4m are
at the corners of a square. They have
accelerations of equal magnitu...

A thin circular plate of mass M and radius R
has its density varying as $$\rho $$(r) = $$\rho $$0r with $$\rho $$0 as
constant and r is the distance f...

The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is 'I(x)'. Which one of the graphs rep...

Two particles A, B are moving on two concentric circles of radii R1 and R2 with equal angular speed $$\omega $$. At t = 0, their positions and directi...

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If ...

Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin ...

The magnitude of torque on a particle of mass 1 kg is 2.5 Nm about the origin. If the force acting on it is 1 N, and the distance of the particle from...

A circular disc D1 of mass M and radius R has two identical discs D2 and D3 of the same mass M and radius R attached rigidly at its opposite ends (see...

A string is wound around a hollow cylinder of mass 5 kg and radius 0.5m. If the string is now pulled with a horizontal force of 40 N, and the cylinder...

A particle is moving along a circular path with a constant speed of 10 ms–1. What is the magnitude of the change in velocity of the particle, when it ...

A slab is subjected to two forces $$\overrightarrow {{F_1}} $$ and $$\overrightarrow {{F_2}} $$ of same magnitude F as shown in the figure. Force $$\...

An equilateral triangle ABC is cut from a thin solid sheet of wood. (see figure) D, E and F are the mid-points of its sides as shown and G is the cent...

Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia o...

To mop-clean a floor, a cleaning machine presses a circular mop of radius R vertically down with a total force F and rotates it with a constant angula...

A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling without slipping, a...

A rod of length 50 cm is pivoted at one end. It is raised such that if makes an angle of 30o from the horizontal as shown and released from rest. Its...

An L-shaped object, made of thin rods of uniform mass density, is suspended with a string as shown in figure. If AB = BC, and the angle made by AB wit...

If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is :

A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment of inertia about z and z' axes will be :
...

Seven identical circular planar disks, each of mass M and radius R are
welded symmetrically as shown. The moment of inertia of the arrangement
about t...

From a uniform circular disc of radius R and mass 9M, a small disc
of radius R/3 is removed as shown in the figure. The moment of
inertia of the remai...

A thin uniform bar of length $$L$$ and mass $$8$$ m lies on a smooth horizontal table. Two point masses m and 2 m are moving in the same horizontal pl...

A thin rod MN, free to rotate in the vertical plane aboutthe fixed end N, is held horizontal. When the end M is released the speed of this end, when t...

A uniform rod $$AB$$ is suspended from a point $$X,$$ at a variable distance $$x$$ from $$A$$, as shown, To make the rod horizontal, a mass $$m$$ is s...

The machine as shown has 2 rods of length1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and t...

A circular hole of radius $${R \over 4}$$ is made in a thin uniform disc having mass M and radius R, as shown in figure. The moment of inertia of the...

Moment of inertia of an equilateral triangular lamina ABC, about the axis
passing through its centre O and perpendicular to its plane is Io as shown ...

In a physical balance working on the principle of moments, when 5 mg weight is placed on the left pan, the beam becomes horizontal. Both the empty pan...

A uniform disc of radius R and mass M is free to rotate only about its axis. A string is wrapped over its rim and a body of mass m is tied to the free...

The moment of inertia of a uniform cylinder of length $$l$$ and radius R about its perpendicular bisector is $$I$$.
What is the ratio $${l \over R}$$ ...

A slender uniform rod of mass M and length $$l$$ is pivoted at one end so that it
can rotate in a vertical plane (see figure). There is negligible fri...

Concrete mixture is made by mixing cement, stone and sand in a rotating
cylindrical drum. If the drum rotates too fast, the ingredients remain stuck t...

In the figure shown ABC is a uniform wire. If centre of mass of wire lies vertically below point A, then $${{BC} \over {AB}}$$ is close to :
...

A cubical block of side 30 cm is moving with velocity 2 ms−1 on a smooth horizontal surface. The surface has a bump at a point O as shown in figure. T...

A roller is made by joining together two cones at their vertices $$0$$. It is kept on two rails $$AB$$ and $$CD$$, which are placed asymmetrically (se...

Distance of the center of mass of a solid uniform cone from its vertex is $$z{}_0$$. If the radius of its base is $$R$$ and its height is $$h$$ then $...

From a solid sphere of mass $$M$$ and radius $$R$$ a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through i...

A bob of mass $$m$$ attached to an inextensible string of length $$l$$ is suspended from a vertical support. The bob rotates in a horizontal circle wi...

A mass $$'m'$$ is supported by a massless string wound around a uniform hollow cylinder of mass $$m$$ and radius $$R.$$ If the string does not slip o...

A hoop of radius $$r$$ and mass $$m$$ rotating with an angular velocity $${\omega _0}$$ is placed on a rough horizontal surface. The initial velocity ...

A thin horizontal circular disc is rotating about a vertical axis passing through its center. An insect is at rest at a point near the rim of the disc...

A mass $$m$$ hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass $$m$$ and radius $$R.$$ Assuming p...

A pulley of radius $$2$$ $$m$$ is rotated about its axis by a force $$F = \left( {20t - 5{t^2}} \right)$$ newton (where $$t$$ is measured in seconds) ...

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 $$\...

Consider a uniform square plate of side $$' a '$$ and mass $$'m'$$. The moment of inertia of this plate about an axis perpendicular to its plane and p...

A thin rod of length $$'L'$$ is lying along the $$x$$-axis with its ends at $$x=0$$ and $$x=L$$. Its linear density (mass/length) varies with $$x$$ as...

A circular disc of radius $$R$$ is removed from a bigger circular disc of radius $$2R$$ such that the circumferences of the discs coincide. The center...

A round uniform body of radius $$R,$$ mass $$M$$ and moment of inertia $$I$$ rolls down (without slipping) an inclined plane making an angle $$\theta ...

Angular momentum of the particle rotating with a central force is constant due to

For the given uniform square lamina $$ABCD$$, whose center is $$O,$$
...

Consider a two particle system with particles having masses $${m_1}$$ and $${m_2}$$. If the first particle is pushed towards the center of mass throug...

A thin circular ring of mass $$m$$ and radius $$R$$ is rotating about its axis with a constant angular velocity $$\omega $$. Two objects each of mass ...

Four point masses, each of value $$m,$$ are placed at the corners of a square $$ABCD$$ of side $$l$$. The moment of inertia of this system about an ax...

A force of $$ - F\widehat k$$ acts on $$O,$$ the origin of the coordinate system. The torque about the point $$(1, -1)$$ is
...

An annular ring with inner and outer radii $${R_1}$$ and $${R_2}$$ is rolling without slipping with a uniform angular speed. The ratio of the forces e...

The moment of inertia of a uniform semicircular disc of mass $$M$$ and radius $$r$$ about a line perpendicular to the plane of the disc through the ce...

A body $$A$$ of mass $$M$$ while falling vertically downloads under gravity breaks into two-parts; a body $$B$$ of mass $${1 \over 3}$$ $$M$$ and a bo...

A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force $$'\,\,\overrightarrow F \,\,'$$ is applied at the point $$...

One solid sphere $$A$$ and another hollow sphere $$B$$ are of same mass and same outer radii. Their moment of inertia about their diameters are respec...

A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which on of the following will not be affected ?

A particle performing uniform circular motion has angular frequency is doubled & its kinetic energy halved, then the new angular momentum is

Let $$\overrightarrow F $$ be the force acting on a particle having position vector $$\overrightarrow r ,$$ and $$\overrightarrow \tau $$ be the tor...

A circular disc $$X$$ of radius $$R$$ is made from an iron plate of thickness $$t,$$ and another disc $$Y$$ of radius $$4$$ $$R$$ is made from an iro...

Initial angular velocity of a circular disc of mass $$M$$ is $${\omega _1}.$$ Then two small spheres of mass $$m$$ are attached gently to diametricall...

A solid sphere, a hollow sphere and a ring are released from top of an inclined plane (frictionless) so that they slide down the plane. Then maximum a...

A particle of mass $$m$$ moves along line PC with velocity $$v$$ as shown. What is the angular momentum of the particle about P?
...

Two identical particles move towards each other with velocity $$2v$$ and $$v$$ respectively. The velocity of center of mass is

Moment of inertia of a circular wire of mass $$M$$ and radius $$R$$ about its diameter is