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General
Easy
Question
A child with mass m is standing at the edge of a disc with moment of inertia I, radius R, and initial angular velocity 
. See figure given below. The child jumps off the edge of the disc with tangential velocity v with respect to the ground. The new angular velocity of the disc is
The correct answer is:
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Physics-
A man is sitting in a smooth groove on a horizontal circular table at the edge by holding a rope joined to the centre. The moment of inertia of table is I. Mass of man = M. Man now pulls the rope so that he comes to the centre. The angular velocity of the table :
A man is sitting in a smooth groove on a horizontal circular table at the edge by holding a rope joined to the centre. The moment of inertia of table is I. Mass of man = M. Man now pulls the rope so that he comes to the centre. The angular velocity of the table :
Physics-General
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A small bead of mass m moving with velocity v gets threaded on a stationary semicircular ring of mass m and radius R kept on a horizontal table. The ring can freely rotate about its centre. The bead comes to rest relative to the ring. What will be the final angular velocity of the system?
A small bead of mass m moving with velocity v gets threaded on a stationary semicircular ring of mass m and radius R kept on a horizontal table. The ring can freely rotate about its centre. The bead comes to rest relative to the ring. What will be the final angular velocity of the system?
Physics-General
Physics-
A block of mass m is attached to a pulley disc of equal mass m, radius r by means of a slack string as shown. The pulley is hinged about its centre on a horizontal table and the block is projected with an initial velocity of 5 m/s. Its velocity when the string becomes taut will be
A block of mass m is attached to a pulley disc of equal mass m, radius r by means of a slack string as shown. The pulley is hinged about its centre on a horizontal table and the block is projected with an initial velocity of 5 m/s. Its velocity when the string becomes taut will be
Physics-General
Physics-
A solid cone hangs from a frictionless pivot at the origin O, as shown. If 
and
are unit vectors, and a, b, and c are positive constants, which of the following forces F applied to the rim of the cone at a point P results in a torque t on the cone with a negative component t Z ?
A solid cone hangs from a frictionless pivot at the origin O, as shown. If and are unit vectors, and a, b, and c are positive constants, which of the following forces F applied to the rim of the cone at a point P results in a torque t on the cone with a negative component t Z ?
Physics-General
Physics-
A sphere is placed rotating with its centre initially at rest in a corner as shown in figure (A) & (B). Coefficient of friction between all surfaces and the sphere is 
. Find the ratio of the frictional force 
by ground in situations (A) & (B).
A sphere is placed rotating with its centre initially at rest in a corner as shown in figure (A) & (B). Coefficient of friction between all surfaces and the sphere is . Find the ratio of the frictional force by ground in situations (A) & (B).
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For the pivoted slender rod of length l as shown in figure, the angular velocity as the bar reaches the vertical position after being released in the horizontal position is
For the pivoted slender rod of length l as shown in figure, the angular velocity as the bar reaches the vertical position after being released in the horizontal position is
Physics-General
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A non uniform rod OA of linear mass density 
(
= const.) is suspended from ceiling with hinge joint O & light string as shown in figure. Find the angular acceleration of rod just after the string is cut.
A non uniform rod OA of linear mass density (= const.) is suspended from ceiling with hinge joint O & light string as shown in figure. Find the angular acceleration of rod just after the string is cut.
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Physics-
A rod hinged at one end is released from the horizontal position as shown in the figure. When it becomes vertical its lower half separates without exerting any reaction at the breaking point. Then the maximum angle ‘
’ made by the hinged upper half with the vertical is :
A rod hinged at one end is released from the horizontal position as shown in the figure. When it becomes vertical its lower half separates without exerting any reaction at the breaking point. Then the maximum angle ‘’ made by the hinged upper half with the vertical is :
Physics-General
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A pulley is hinged at the centre and a massless thread is wrapped around it. The thread is pulled with a constant force F starting from rest. As the time increases,
A pulley is hinged at the centre and a massless thread is wrapped around it. The thread is pulled with a constant force F starting from rest. As the time increases,
Physics-General
Physics-
Two light vertical springs with equal natural lengths and spring constants k1 and k2 are separated by a distance l. Their upper ends are fixed to the ceiling and their lower ends to the ends A and B of a light horizontal rod AB. A vertical downwards force F is applied at point C on the rod. AB will remain horizontal in equilibrium if the distance AC is
Two light vertical springs with equal natural lengths and spring constants k1 and k2 are separated by a distance l. Their upper ends are fixed to the ceiling and their lower ends to the ends A and B of a light horizontal rod AB. A vertical downwards force F is applied at point C on the rod. AB will remain horizontal in equilibrium if the distance AC is
Physics-General
Physics-
The spool shown in figure is placed on rough horizontal surface and has inner radius r and outer radius R. The angle between the applied force and the horizontal can be varied. The critical angle () for which the spool does not roll and remains stationary is given by
The spool shown in figure is placed on rough horizontal surface and has inner radius r and outer radius R. The angle between the applied force and the horizontal can be varied. The critical angle () for which the spool does not roll and remains stationary is given by
Physics-General
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A uniform rod of length L and weight W is suspended horizontally by two vertical ropes as shown. The first rope is attached to the left end of the rod while the second rope is attached a distance L 4 from the right end. The tension in the second rope is
A uniform rod of length L and weight W is suspended horizontally by two vertical ropes as shown. The first rope is attached to the left end of the rod while the second rope is attached a distance L 4 from the right end. The tension in the second rope is
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Physics-
A uniform cylinder rests on a cart as shown. The coefficient of static friction between the cylinder and the cart is 0.5. If the cylinder is 4 cm in diameter and 10 cm in height, which of the following is the minimum acceleration of the cart needed to cause the cylinder to tip over?
A uniform cylinder rests on a cart as shown. The coefficient of static friction between the cylinder and the cart is 0.5. If the cylinder is 4 cm in diameter and 10 cm in height, which of the following is the minimum acceleration of the cart needed to cause the cylinder to tip over?
Physics-General
Physics-
A uniform ladder of length 5m is placed against the wall as shown in the figure. If coefficient of friction 
is the same for both the walls, what is the minimum value of for it not to slip?
A uniform ladder of length 5m is placed against the wall as shown in the figure. If coefficient of friction is the same for both the walls, what is the minimum value of for it not to slip?
Physics-General
Physics-
A smooth rod of length 
is kept inside a trolley at an angle as shown in the figure. What should be the acceleration a of the trolley so that the rod remains in equilibrium with respect to it?
A smooth rod of length is kept inside a trolley at an angle as shown in the figure. What should be the acceleration a of the trolley so that the rod remains in equilibrium with respect to it?
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