Systems of Part...

Two solid cylinders P and Q of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder P has most of its mass concentrated near its surface, while Q has most of its mass concentrated near the axis. Which statements (s) is (are) correct ?

A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision

Look at the drawing given in the figure, which has been drawn with ink of uniform line thickness. The mass of ink used to draw each of the two inner circles and each of the two line segments is m. The mass of the ink used to draw the outer circle is 6 m.
The coordinates of the centres of the different parts are outer circle (0, 0) left inner circle (– a, a), right inner circle (a, a), vertical line (0, 0) and horizontal line (0, –a). The y – coordinate of the centre of mass of the ink in this drawing is

A pulley fixed to the ceiling carries a string with blocks of masses m and 3m attached to its ends. The masses of string and pulley are negligible. When the system is released, the acceleration of centre of mass will be

The figure shows a system consisting of (i) a ring of outer radius 3R rolling clockwise without slipping on a horizontal surface with angular speed w and (ii) an inner disc of radius 2R rotating anti–clockwise with angular speed w/ 2 .
The ring and disc are separated by frictionless ball bearings. The system is in the x–z plane. The point P on the inner disc is at a distance R from the origin, where OP makes an angle of 30° with the horizontal. Then with respect to the horizontal surface,

A T shaped object with dimensions shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C.

Three identical spheres of mass M each are placed at the corners of an equilateral triangle of side 2 m. Taking one of the corner as the origin, the position vector of the centre of mass is