IIT-JEE 2012 Paper 1 Offline | Rotational Motion Question 41 | Physics

1

IIT-JEE 2012 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

A small mass m is attached to a massless string whose other end is fixed at P as shown in the figure. The mass is undergoing circular motion in the xy-plane with centre at O and constant angular speed $$\omega$$. If the angular momentum of the system, calculated about O and P are denoted by $${\overrightarrow L _O}$$ and $${\overrightarrow L _P}$$, respectively, then

IIT-JEE 2012 Paper 1 Offline Physics - Rotational Motion Question 19 English

A

$${\overrightarrow L _O}$$ and $${\overrightarrow L _P}$$ do not vary with time.

B

$${\overrightarrow L _O}$$ varies with time while $${\overrightarrow L _P}$$ remains constant.

C

$${\overrightarrow L _O}$$ remains constant while $${\overrightarrow L _P}$$ varies with time.

D

$${\overrightarrow L _O}$$ and $${\overrightarrow L _P}$$ both vary with time.

2

IIT-JEE 2012 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

A thin uniform rod, pivoted at O, is rotating in the horizontal plane with constant angular speed $$\omega$$, as shown in the figure. At time t = 0, a small insect starts from O and moves with constant speed v, with respect to the rod towards the other end. It reaches the end of the rod at t = T and stops. The angular speed of the system remains $$\omega$$ throughout. The magnitude of the torque (|$$\tau$$|) about O, as a function of time is best represented by which plot ?

IIT-JEE 2012 Paper 1 Offline Physics - Rotational Motion Question 20 English

A

B

IIT-JEE 2012 Paper 1 Offline Physics - Rotational Motion Question 20 English Option 2

C

IIT-JEE 2012 Paper 1 Offline Physics - Rotational Motion Question 20 English Option 3

D

IIT-JEE 2012 Paper 1 Offline Physics - Rotational Motion Question 20 English Option 4

3

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant $$k$$ which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity $${\overrightarrow V _0} = {V_0}\widehat i$$. the coefficient of friction is $$\mu$$.

IIT-JEE 2008 Paper 2 Offline Physics - Rotational Motion Question 8 English Comprehension

The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is :

A

$$ - kx$$

B

$$ - 2kx$$

C

$$ - {{2kx} \over 3}$$

D

$$ - {{4kx} \over 3}$$

4

IIT-JEE 2008 Paper 2 Offline

MCQ (Single Correct Answer)

+3

-1

A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant $$k$$ which are fixed to the wall as shown in the figure. The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre. The axle is massless and both the springs and the axle are in a horizontal plane. The unstretched length of each spring is L. The disk is initially at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocity $${\overrightarrow V _0} = {V_0}\widehat i$$. the coefficient of friction is $$\mu$$.

IIT-JEE 2008 Paper 2 Offline Physics - Rotational Motion Question 9 English Comprehension

The centre of mass of the disk undergoes simple harmonic motion with angular frequency $$\omega$$ equal to:

A

$$\sqrt {{k \over M}} $$

B

$$\sqrt {{{2k} \over M}} $$

C

$$\sqrt {{{2k} \over {3M}}} $$

D

$$\sqrt {{{4k} \over {3M}}} $$