A system consists of two particles of masses $m_1$ and $m_2$. If the particle of mass $m_1$ is moved towards the centre of mass through a distance $d$, then the distance the second particle should be moved, so as to keep the centre of mass at the same position is

Particle $A$ moving with a velocity $v=10 \mathrm{~m} / \mathrm{s}$ experienced a head on collision with a stationary particle $B$ of the same mass. As a result of collision, the kinetic energy of the system decreased by $1 \%$. The speed of particle $A$ after collision is

Assertion (A) In an elastic collision of two billiard balls, both kinetic energy and linear momentum remain conserved.

Reason (R) During the collision of the balls, as the collision is elastic there is no exchange of energy. Therefore, both energy and momentum are conserved. The correct option among the following is

A moving particle collides with a stationary particle of mass $\frac{1}{n}$ times the mass of moving particle, the fraction of its kinetic energy transferred to the stationary particle is