Systems of Part...

A solid sphere of mass 1 kg radius 10 cm rolls down an inclined plane of height 7 m. The velocity of its centre as it reaches the ground level is

A ring starts to roll down the inclined plane of height h without slipping. The velocity with which it reaches the

A ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards right as shown. Relative to its initial with respect to the table, the ball
(1) Remains stationary if there is no friction between the paper and the ball.
(2) Moves to the left and starts rolling backwards, i. e., to the left if there is a friction between the paper and the ball.
(3) Moves forward, i. e., in the direction in which the paper is pulled. Here, the correct statements is/are

Two particles A and B initially at rest move towards each other under a mutual force of attraction. At the instant when the speed of A is v and the speed of B is 2v, the speed of centre of mass of the system is

A disc is rolling (without slipping) on a horizontal surface. C is its centre and Q and P are two points equidistant from C. Let v_P, v_Q and v_C be the magnitude of velocities of points P, Q and C respectively, then

One quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is

A thin wire of length L and uniform linear mass density ρ is bent into a circular loop with centre at O as shown. The moment of inertia of the loop about the axis. XX\' is

Two discs of same thickness but of different radii are made of two different materials such that their masses are same. The densities of the materials are in the ratio 1 : 3. The moments of inertia of these discs about the respective axes passing through their centres and perpendicular to their planes will be in the ratio

Two point masses of 0.3 kg and 0.7 kg are fixed at the ends of a rod of length 1.4 m and of negligible mass. The rod is set rotating about an axis perpendicular to its length with a uniform angular speed. The point on the rod through which the axis should pass in order that the work required for rotation of the rod is minimum, is located at a distance of

A pulley of radius 2m is rotated about its axis by a force F = (20t – 5t²) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m², the number of rotations made by the pulley before its direction of motion if reversed, is