If two particles of masses `m_(1)` and `m_(2)` are projected vertically upwards with speed `v_(1)` and `v_(2)`, then the acceleration of the centre of mass of the system is

The velocities of two particles of masses m_(1) and m_(2) relative to an observer in an inertial frame are v_(1) and v_(2) . Determine the velocity of the center of mass relative to the observer and the velocity of each particle relative to the center of mass.

Two particles having masses m_(1) and m_(2) are moving with velocities vec(V)_(1) and vec(V)_(2) respectively. vec(V)_(0) is velocity of centre of mass of the system. (a) Prove that the kinetic energy of the system in a reference frame attached to the centre of mass of the system is KE_(cm) = (1)/(2)mu V_(rel)^(2) . Where mu=(m_(1)m_(2))/(m_(1)+m_(2)) and V_(rel) is the relative speed of the two particles. (b) Prove that the kinetic energy of the system in ground frame is given by KE=KE_(cm)+(1)/(2)(m_(1)+m_(2))V_(0)^(2) (c) If the two particles collide head on find the minimum kinetic energy that the system has during collision.

A stationary particle explodes into two particle of a masses m_(1) and m_(2) which move in opposite direction with velocities v_(1) and v_(2) . The ratio of their kinetic energies E_(1)//E_(2) is

A stationary particle explodes into two particle of a masses m_(1) and m_(2) which move in opposite direction with velocities v_(1) and v_(2) . The ratio of their kinetic energies E_(1)//E_(2) is

Two particles of equal mass 'm' are projected from the ground with speed v_(1) and v_(2) at angles theta_(1) and theta_(2) at the same times as shown in figure. The centre of mass of the two particles.

Two particles of equal mass 'm' are projected from the ground with speed v_(1) and v_(2) at angles theta_(1) and theta_(2) at the same times as shown in figure. The centre of mass of the two particles.

Two particles of mass m_(1) and m_(2) are projected from the top of a tower. The particle m_(1) is projected vertically downward with speed u and m_(2) is projected horizontally with same speed. Find acceleration of CM of system of particles by neglecting the effect of air resistance.

Two particles of mass m_(1) and m_(2) are projected from the top of a tower. The particle m_(1) is projected vertically downward with speed u and m_(2) is projected horizontally with same speed. Find acceleration of CM of system of particles by neglecting the effect of air resistance.

Two particles of mass m_(1) and m_(2) are projected from the top of a tower. The particle m_(1) is projected vertically downward with speed u and m_(2) is projected horizontally with same speed. Find acceleration of CM of system of particles by neglecting the effect of air resistance.