Two balls $A$ and $B$ having masses $1\, kg$ and $2\, kg$, moving with speeds $21\, m/s$ and $4\, m/s$ respectively in opposite direction, collide head on. After collision Amoves with a speed of $1\, m/s$ in the same direction, then the coefficient of restitution is
$0.1$
$0.2$
$0.4$
None
In the figure shown, the two identical balls of mass $M$ and radius $R$ each, are placed in contact with each other on the frictionless horizontal surface. The third ball of mass $M$ and radius $R/2$, is coming down vertically and has a velocity $= v_0$ when it simultaneously hits the two balls and the smaller ball does not stop after collision, but continues to move downwards with $a$ speed $= v_0/2$, after the collision. Then, the speed of each bigger ball after collision is
At high altitude, a body explodes at rest into two equal fragments with one fragment receiving horizontal velocity of $10 \,m/s$. Time taken by the two radius vectors connecting point of explosion to fragments to make $90^o $ is ............ $\mathrm{s}$
A moving particle of mass $m,$ makes a head on elastic collision with another particle of mass $2\,m,$ which is initially at rest. The percentage loss in energy of the colliding particle on collision, is close to .................. $\%$
$Assertion$ : If collision occurs between two elastic bodies their kinetic energy decreases during the time of collision.
$Reason$ : During collision intermolecular space decreases and hence elastic potential energy increases.
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?