HARD
JEE Advanced
IMPORTANT
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A slender rod of mass M and length L rests on a horizontal frictionless surface. The rod is pivoted about one of its ends. The impulse of the force exerted on the rod by the pivot when the rod is struck by a blow of impulse J perpendicular to the rod at other end is

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Important Questions on Rigid Body Dynamics: Part 2

EASY
JEE Advanced
IMPORTANT
A solid cylinder of mass M and radius R is resting on a horizontal platform (which is parallel to the x-y plane) with its axis fixed along Y -axis and free to rotate about its axis. The platform is given a motion in the X -direction given by x=Acos(ωt). There is no slipping between the cylinder and the platform. The maximum torque acting on the cylinder during its motion is
EASY
JEE Advanced
IMPORTANT
A uniform circular disc of radius r is placed on a rough horizontal surface and given a linear velocity v0 and angular velocity ω as shown. The disc comes to rest after moving some distance to the right. It follows that:
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EASY
JEE Advanced
IMPORTANT
Velocity of the centre of a small cylinder is v . There is no slipping anywhere. The velocity of the centre of the larger cylinder is:
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HARD
JEE Advanced
IMPORTANT

A system of uniform cylinders and plates is shown in figure. All the cylinders are identical and there is no slipping at any contact. Velocity of lower & upper plate is V and 2V respectively as shown in figure. Then the ratio of angular speed of the upper cylinders to lower cylinders is

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EASY
JEE Advanced
IMPORTANT
The spool shown in the figure is placed on a rough horizontal surface and has inner radius r and outer radius R . The angle θ between the applied force and the horizontal can be varied. The critical angle (θ) for which the spool does not roll and remains stationary is given by:
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MEDIUM
JEE Advanced
IMPORTANT

A disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in the figure. At any instant, for the lowermost point of the disc

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MEDIUM
JEE Advanced
IMPORTANT

An object of mass M and radius R is performing pure rolling motion on a smooth horizontal surface under the action of a constant force F as shown in figure. The object may be :

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MEDIUM
JEE Advanced
IMPORTANT
A solid cylinder is placed on the end of an inclined plane. It is found that the plane can be tipped at an angle θ before the cylinder starts to slide. When the cylinder turns on its sides and is allowed to roll, it is found that the steepest angle at which the cylinder performs pure rolling is ϕ. The ratio tanϕ/tanθ is