Starting from the centre of the earth having radius r, the variation of g (acceleration due to gravity) is shown by

A light rod of length l has two masses m₁ and mattached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is :

A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation (E_sphere / E cylinder) will be :

Two rotating bodies A and B of masses m and 2m with moments of inertia I_A and I_B (I_B > I_A) have equal kinetic energy of rotation. If L_A and L_B be their angular momenta respectively, then

Two identical balls A and B having velocities of 0.5 m/s and –0.3 m/s respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be