System of Particles and Rotational Motion

The center of mass of a system of particles is the point where:

If two particles of masses m and 2m are located at positions x=0 and x=3 m respectively, the position of the center of mass is:

The moment of inertia of a uniform thin rod of length L about an axis passing through its center and perpendicular to its length is:

Which of the following quantities is NOT conserved in a system of particles when internal forces act?

A solid sphere and a solid cylinder, both of mass M and radius R, roll down an inclined plane without slipping. Which one reaches the bottom first?

The angular momentum of a particle moving in a circle of radius r with linear velocity v about the center is:

If the angular velocity of a rotating body is doubled, its kinetic energy becomes:

Two particles of masses m and 3m are moving with velocities v and 2v respectively in the same direction. The velocity of the center of mass is:

A uniform disc of mass M and radius R rotates about its axis with angular velocity ω. Its rotational kinetic energy is:

A particle moves in a circle of radius R with constant speed v. The torque about the center of the circle is: