Centre of Mass Frame

Two particles of masses m and 3m approach each other with different velocities. After collision, the particle of mass m has velocity vec( v) in their centre of mass frame. Velocity of particle of mass 3m in the centre of mass frame is

Two blocks are connected by a spring and given velocity v_(1) and v_(2) as shown in figure when spring is unstrected Statement-1: In centre of mass frame, both the blocks come to rest simultaneously Statement-2: Momentum of a system in centre of mass frame is always zero.

STATEMENT-1 : The relation vectau=(dvecL)/(dt) is applicable in centre of mass frame, even though the centre of mass is accelerating. and STATEMENT-2 : The relation vectau=(dvecL)/(dt) can be directly applied in a non-inertial frame.

A billiard ball collides elastically with an identical stationary ball. The collision is not head on. Show that the directions of motion of the two balls are at right angles after the collision. Solve the problem in centre of mass frame as well as in lab frame.

Statement-1: In centre of mass frame the linear momentum of system is conserved only if no external forces are present Statement-2: In presence of external force, the centre of mass has acceleration in inertial frame equal to (Sigmavec(F)_(ext))/(m_(total))

Statement-1 : Total linear momentum of system in centre of mass frame is zero only when there is no net external force. Statement-2 : Total linear momentum of system is conserved in absence of net external force.

Two blocks of masses 5 kg and 2 kg are placed on a frictionless surface and connected by a spring. An external kick gives a velocity of 14 m//s to the heavier block in the direction of lighter one. The magnitudes of velocities of two blocks in the centre of mass frame after the kick are, respectively,

Two identical non-relativitic partcles A and B move at right angles to each othre, processing de Broglie wavelengths lamda_1 and lamda_2 , respectively. The de Broglie wavelength of each particle in their centre of mass frame of reference is

Total work of pseudo forces in center of mass frame. Show that total work done in center of mass frame on all the particles of a system by pseudo forces due to acceleration of mass center is zero.