A uniform solid cone of height $h$ and base radius $r$ rolls without slipping on a horizontal plane. The ratio of its rotational kinetic energy to its total kinetic energy is:

The center of mass of a hollow sphere of uniform density is located:

A body is in equilibrium under the influence of gravity. Which of the following is true about its center of gravity?

A small disc of radius 2 cm is cut from a disc of radius 6 cm. If the distance between their centres is 3.2 cm, what is the shift in the centre of mass of the disc?

A man of mass M stands at one end of a plank of mass m and length L, which lies on a smooth horizontal surface. The man walks to the other end of the plank. What is the displacement of the plank?

The centre of mass of a system of three particles of masses 1g,2g and 3g is taken as the origin of a coordinate system. The position vector of a fourth particle of mass 4g such that the centre of mass of the four particle system lies at the point (1, 2, 3) is $\alpha \left( {\hat i + 2\hat j + 3\hat k} \right)$, where $\alpha$ is a constant. The value of $\alpha$ is

Particles of masses m, 2m, 3m…… grams are placed on the same line at distances $l,2l,3l....nl\,cm$ from a fixed point. The distance of centre of mass of the particles from the fixed point in centimetre is

A loded spring gun of mass M fires a shot of mass m with a velocity v at an angle of elevation $heta$. The gun was initially at rest on a horizontal frictionless surface. After firing, the centre of mass of gun-shot system

A system consists of three particles of masses 1 kg, 2 kg, and 3 kg located at the vertices of an equilateral triangle of side 'a'. The distance of the center of mass from the 1 kg mass is:

A uniform rod of length 8 m and mass 30 kg has two point masses of 5 kg and 10 kg attached at its ends. The distance of the center of mass of the system from the 5 kg mass is:

Two particles of masses $m_1$ and $m_2$ are connected by a massless rigid rod of length $L$. The system rotates with a constant angular velocity $\omega$ about an axis perpendicular to the rod and passing through its center of mass. The kinetic energy of the system is: