Four identical particles each of mass $m$ are kept at the four corners of a square of side $a$. If one of the particles is removed, the shift in the position of the centre of mass is

A bomb of mass 16 kg explodes into two pieces of masses 4 kg and 12 kg . The velocity of the 12 kg mass is $4 \mathrm{~ms}^{-1}$. The kinetic energy of the second piece is

A ball falls freely from a height $h$ on a rigid horizontal plane. If the coefficient of restitution is $e$, then the total distance travelled by the ball before hitting the plane second time is

Two blocks of masses 2 kg and 1 kg are tied to the ends of a string which passes over a light frictionless pulley. The blocks are held at the same horizontal level and then released suddenly. The distance traversed by their centre of mass in 2 sec is

(acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )