$A$ particle of mass $m$ is moving in a horizontal circle of radius $r$ under a centripetal force equal to $-K/r^2$,where $K$ is a constant. The total energy of the particle is

$A$ particle of mass $m$ is at rest in a train moving with constant velocity with respect to the ground. Now,the particle is accelerated by a constant force $F_0$ acting along the direction of motion of the train for time $t_0$. $A$ girl in the train and a boy on the ground measure the work done by this force. Which of the following are $INCORRECT$?

$A$ ball of mass $m = 60 \text{ g}$ is shot with speed $v_0 = 22 \text{ m/s}$ into the barrel of a spring gun of mass $M = 240 \text{ g}$ initially at rest on a frictionless surface. The ball sticks in the barrel at the point of maximum compression of the spring. What fraction of the initial kinetic energy of the ball is now stored in the spring?

Four particles $A, B, C$ and $D$ of equal mass $m$ are placed at four corners of a square. They move with equal uniform speed $v$ towards the intersection of the diagonals. After collision,$A$ comes to rest,$B$ traces its path back with the same speed $v$,and $C$ and $D$ move with equal speeds $v'$. What is the velocity of $C$ after collision?

$A$ smooth sphere of mass $m$ moving with velocity $u$ collides with another smooth sphere of mass $2m$ at rest. What is the range of the velocity $v$ of the second sphere after the collision?

If a skater of mass $3 \,kg$ has an initial speed of $32 \,m/s$ and a second skater of mass $4 \,kg$ has a speed of $5 \,m/s$. After a perfectly inelastic collision,they move together with a speed of $5 \,m/s$. Calculate the loss in kinetic energy.