A train is moving at a constant speed $V$. When its driver observes another train in front of him on the same track and moving in the same direction with constant speed $u$. If the distance between the trains be $x$, then what should be the minimum retardation of the train so as to avoid collision?
$(V + u)^2\,/x$
$(V -u)^2\,/x$
$(V + u)^2\,/2x$
$(V -u)^2\,/2x$
The friction coefficient between the horizontal surface and each of the block shown in figure is $0.2.$ The collision between the blocks is perfectly elastic. What is the separation between the blocks when they come to rest :- .............. $\mathrm{cm}$
A body falling from a height of $10\,m$ rebounds from hard floor. If it loses $20\%$ energy on the impact, then coefficient of restitution is
Two pendulums with identical bobs and lengths are suspended from a common support such that in rest position the two bobs are in contact (figure). One of the bobs is released after being displaced by $10^o$ so that it collides elastically head-on with the other bob.
$(a)$ Describe the motion of two bobs.
$(b)$ Draw a graph showing variation in energy of either pendulum with time, for $0\, \leqslant \,t\, \leqslant \,2T$, where $T$ is the period of each pendulum.
A ball of mass $m$ moving with velocity $v$ collides head-on with the second ball of mass $m$ at rest. If the coefficient of restitution is $e$ and velocity of first ball after collision is $v_1$ and velocity of second ball after collision is $v_2$ then
What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of $5$ times its mass? (Assume the collision to be head-on elastic collision)