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

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 ?

A
B
C
D
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 $$\mu$$.

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 $$\mu$$.

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