Rotational Motion MCQ Level - 1 - Class 11 MCQ

A yo-yo, arranged as shown, rests on a frictionlesssurface. When a force F is applied to the string, the yo-yo

Velocity of the centre of a small cylinder is v. There isno slipping any where. The velocity of the centre of the larger cylinder

The figure shows a uniform rod lying along the x-axis.The locus of all the points lying on the x-y plane, aboutwhich the moment of inertia of the rod is same as thatabout O, is

Find the minimum height of the obstacle so that the sphere can stay in equilibrium.

The spool shown in the figure is placed on a roughhorizontal surface and has inner radius r and outerradius R. The angle θ between the applied force and the horizontal can be varied. The critical angle ( θ ) forwhich the spool does not roll and remains stationaryis given by

A small bead of mass m moving with velocity v getsthreaded on a stationary semicircular ring of mass mand radius R kept on a horizontal table. The ring canfreely rotate about its centre. The bead comes to restrelative to the ring. What will be the final angular velocityof the system?

A sphere is placed rotating with its centre initially at rest in a corner as shown in figures (a) and (b). Coefficient of friction between all surfaces and the sphere is 1/3. Find the ratio of the friction forces f_a / f_b by ground in situations (a) and (b).

A block of mass m is attached to a pulley disc of equalmass m radius r by means of a slack string as shown.The pulley is hinged about its centre on a horizontaltable and the block is projected with an initial velocityof 5 m/s. Its velocity when the string becomes tautwill be

Four rods of side length / have been hinged to form arhombus. Vertex A is fixed to a rigid support, vertex Cis being moved along the x-axis with constant velocitywas shown in Fig.The rate at which vertex B is nearingthe x-axis at the moment the rhombus is in the form of a square is

In the figure shown, the instantaneous speed of end Aof the rod is v’ to the left. The angular velocity of the rodof length L must be

Two blocks each of mass m and a cylinder C areconnected as shown in Fig. Angular acceleration ofthe cylinder C of radius R is (all strings and pulley areideal):

A uniform rod of mass m and length / is fixed from point A, vhich is at a distance l/4 from one end asshown in the figure. The rod is free to rotate in a verticalplane. The rod is released from the horizontal position.What is the reaction at the hinge, when kinetic energy of the rod is maximum?

A uniform pole of length L and mass M is pivoted onthe ground with a frictionless hinge. The pole makesan angle qwith the horizontal. The moment of inertiaof the pole about one end is (1/3) ML2. If it starts fallingfrom the position shown in the accompanying figure,the linear acceleration of the free end of the poleimmediately after release would be

In the figure shown, a ring A is initially rolling withoutsliding with a velocity v on the horizontal surface of thebody B (of same mass as A). All surfaces are smooth.B has no initial velocity. What will be the maximumheight reached by A on B?

Two points of a rod move with velocities 3v and vperpendicular to the rod and in the same directionseparated by a distance 'r'. The angular velocity of therod is

A sphere is released on a smooth inclined plane fromthe top.When it moves down, its angular momentum is

In the figure shown, a ball without sliding on a horizontalsurface. It ascends a curved track up to height h and returns. The value of h is h₁ for sufficiently rough curved track to avoid sliding and is h₂ for smooth curved track,then

A ring of radius R rolls without sliding with a constantvelocity. The radius of curvature of the path followed byany particle of the ring at the highest point of its pathwill be

A uniform ring of radius R is given a back spin of angularvelocity V₀/2R and thrown on a horizontal rough surfacewith velocity of centre to be V₀. The velocity of the centreof the ring when it starts pure rolling will be

A disc is performing pure rolling on a smooth stationarysurface with constant angular velocity as shown in Fig.At any instant, for the lower most point of the disc,

A particle of mass ‘m’ is rigidly attached at ‘A’ to a ringof mass '3m' and radius ‘r' The system is released fromrest and rolls without sliding. The angular accelerationof ring just after release is

A solid sphere, a hollow sphere and a disc, all havingthe same mass and radius, are placed at the top of anincline and released. The friction coefficients betweenthe objects and the incline are same and not sufficientto allow pure rolling. The least time will be taken inreaching the bottom by

In the previous problem, the smallest kinetic energy atthe bottom of the incline will be achieved by

An equilateral prism of mass m rests on a roughhorizontal surface with coefficient of friction μ. Ahorizontal force F is applied on the prism as shown inFig. If the coefficient of friction is sufficiently high so that the prism does not slide before toppling. theminimum force required to topple the prism is

A unit form disc of radius R lies in the x-y plane, with its centre at origin. Its moment of inertia about z-axis is equal to its moment of inertia about line y = x + c. The value of c will be

A mass m is moving at speed v perpendicular to a rodof length a and mass M = 6 m which pivots around africtionless axle running through its centre. It strikesand sticks to the end of the rod. The moment of inertiaof the rod about its centre is Md²/12. Then the angularspeed of the system just after the collision is

In the figure shown, a small ball of mass ‘m' can movewithout sliding in a fixed semicircular track of radius R in a vertical plane. It is released from the top. Theresultant force on the ball at the lowest point of thetrack is