HARD
JEE Main
IMPORTANT
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Moment of inertia of an equilateral triangular lamina , about the axis passing through its centre and perpendicular to its plane is as shown in the figure. A cavity is cut out from the lamina, where are the mid points of the sides. Moment of inertia of the remaining part of lamina about the same axis is:
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Important Questions on Rotational Motion
EASY
JEE Main
IMPORTANT
In a physical balance working on the principle of moments, when weight is placed on the left pan, the beam becomes horizontal. Both the empty pans of the balance are of equal mass. Which of the following statements is correct?
MEDIUM
JEE Main
IMPORTANT
A circular hole of radius is made in a thin uniform disc having mass and radius , as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point and perpendicular to the plane of the disc is-
MEDIUM
JEE Main
IMPORTANT
A cubical block of side is moving with velocity on a smooth horizontal surface. The surface has a bump at a point as shown in the figure. The angular velocity (in rad/s) of the block immediately after it hits the bump, is :
HARD
JEE Main
IMPORTANT
A particle of mass m is moving along the side of a square of side 'a', with a uniform speed in the x-y plane as shown in the figure:
Which of the following statements is false for the angular momentum about the origin?
MEDIUM
JEE Main
IMPORTANT
A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to:
HARD
JEE Main
IMPORTANT
In the figure shown is a uniform wire. If the center of mass of the wire lies vertically below point , then is close to
EASY
JEE Main
IMPORTANT
Consider a thin uniform square sheet made of a rigid material. If its side is , mass m and moment of inertia about one of its diagonals, then:
HARD
JEE Main
IMPORTANT
A block of mass is connected to a spring of unknown spring constant k. It is compressed to a distance from its equilibrium position and released from rest. After approaching half the distance from the equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with velocity . The total initial energy of the spring is:
