1
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 25 English

A
IIT-JEE 2012 Paper 1 Offline Physics - Rotational Motion Question 25 English Option 1
B
IIT-JEE 2012 Paper 1 Offline Physics - Rotational Motion Question 25 English Option 2
C
IIT-JEE 2012 Paper 1 Offline Physics - Rotational Motion Question 25 English Option 3
D
IIT-JEE 2012 Paper 1 Offline Physics - Rotational Motion Question 25 English Option 4
2
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 13 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
$$ - {{4kx} \over 3}$$
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 14 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
$$\sqrt {{{4k} \over {3M}}} $$
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 12 English Comprehension

The maximum value of V$$_0$$ for which the disk will roll without slipping is:

A
$$\mu g\sqrt {{M \over k}} $$
B
$$\mu g\sqrt {{M \over {2k}}} $$
C
$$\mu g\sqrt {{{3M} \over k}} $$
D
$$\mu g\sqrt {{{5M} \over {2k}}} $$
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