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:

If the net external force on a system of particles is zero, what can be said about the velocity of the center of mass?

Two spherical bodies of mass ‘M’ and ‘5M’ and radii ‘R’ and ‘2R’ released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body before collision is

Two particles of masses ‘${m_1}$ ’ and ‘ ${m_2}$’ initially at rest start moving towards each other under their mutual force of attraction. The speed of the centre of mass of any time ‘$t$’. When they are at a distance ‘$r$’ part is

A thin uniform disc of mass $M$ and radius $R$ has a small hole of radius $r$ drilled at a distance $d$ from its center. The moment of inertia of the remaining portion about an axis passing through the center of the original disc and perpendicular to its plane is:

A uniform rod of length L is bent into the shape of a semicircle. Where is the center of mass of this semicircular rod located?

Three masses of 5 kg, 10 kg, and 15 kg are placed at positions x = 0 m, x = 2 m, and x = 4 m respectively along a straight line. Find the position of the center of mass of the system.

The center of mass of three particles of masses 1 kg, 2 kg and 3 kg at (3, 3, 3) with reference to a fixed coordinate system. Where should a fourth particle of mass 4 kg should be placed, so that the center of mass of the system of all particles shifts to a point (1, 1, 1)?

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:

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

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