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1.
The instantaneous angular-position of a point on a rotating wheel is given by the equation 
. The torque on the wheel becomes zero at
. The torque on the wheel becomes zero at
2.
A disc is rotating with an angular speed of 
. If a child sits on it, which of the following is conserved
. If a child sits on it, which of the following is conserved
3.
Look at the drawing given in the figure, which has been drawn with ink of uniform line-thickness. The mass of ink used to draw each of the two inner circles, and each of the two line segments is 
. The mass of ink used to draw the outer circle is 6. The coordinates of the centres of the different parts are : outer circle (0, 0) left inner circle (-
), right inner circle () vertical line (0, 0) and horizontal line (0, -
). The 
- coordinate of the centre of mass of the ink in the drawing is
. The mass of ink used to draw the outer circle is 6. The coordinates of the centres of the different parts are : outer circle (0, 0) left inner circle (-), right inner circle () vertical line (0, 0) and horizontal line (0, -). The - coordinate of the centre of mass of the ink in the drawing is
4.
The moments of inertia of two freely rotating bodies 
and 
are 
and 
respectively. 
and their angular momenta are equal. If 
and 
are their kinetic energies, then
and are and respectively. and their angular momenta are equal. If and are their kinetic energies, then
5.
Moment of inertia of big drop in 
. If 8 droplets are formed from big drop, then moment of inertia of small droplet is
. If 8 droplets are formed from big drop, then moment of inertia of small droplet is
6.
A thin wire of mass 
and length 
is bent to form a circular ring. The moment of inertia about its axis is
and length is bent to form a circular ring. The moment of inertia about its axis is
7.
A wheel of mass 8 kg and radius 40 cm is rolling on a horizontal road with angular velocity of 
. The moment of inertia of the wheel about its axis is 
. Total KE of wheel is
. The moment of inertia of the wheel about its axis is . Total KE of wheel is
8.
The two bodies of mass 
and 
respectively are tied to the ends of a massless string, which passes over a light and frictionless pulley. The masses are initially at rest and the released. Then acceleration of the centre of mass of the system is
and respectively are tied to the ends of a massless string, which passes over a light and frictionless pulley. The masses are initially at rest and the released. Then acceleration of the centre of mass of the system is
9.
Three identical blocks 
and 
are placed on horizontal frictionless surface. The blocks and are at rest. But is approaching towards with a speed 10 
. The coefficient of restitution for all collisions is 0.5. The speed of the block just after collision is
and are placed on horizontal frictionless surface. The blocks and are at rest. But is approaching towards with a speed 10 . The coefficient of restitution for all collisions is 0.5. The speed of the block just after collision is
10.
A 
shaped object with dimension shown in the figure, is lying on a smooth floor. A force F is applied at the point 
parallel to 
, such that the object has only the translational motion without rotation. Find the location of with respect to .
shaped object with dimension shown in the figure, is lying on a smooth floor. A force F is applied at the point parallel to , such that the object has only the translational motion without rotation. Find the location of with respect to .