$A$ man who is running has half the kinetic energy of the boy of half his mass. The man speeds up by $1 \, m/s$ and then has the same kinetic energy as the boy. The original speed of the man was
$\sqrt 2 \,m/s$
$( \sqrt 2 - 1)\,m/s$
$2\, m/s$
$(\sqrt 2 + 1)\, m/s$
A basket and its contents have mass $M$. A monkey of mass $2M$ grabs the other end of the rope and very quickly (almost instantaneously) accelerates by pulling hard on the rope until he is moving with a constant speed of $v_{m/r} = 2ft/s$ measured relative to the rope. The monkey then continues climbing at this constant rate relative to the rope for $3$ seconds. How fast is the basket rising at the end of the $3$ seconds? Neglect the mass of the pulley and the rope. (given : $g = 32ft/s^2$)
The variation of force $F$ acting on a body moving along $x$-axis varies with its position $(x)$ as shown in figure The body is in stable equilibrium state at
A ball moving with velocity $2\, m/s$ collides head on with another stationary ball of double the mass. If the coefficient of restitution is $0.5$, then their velocities (in $m/s$) after collision will be
$A$ & $B$ are blocks of same mass $m$ exactly equivalent to each other. Both are placed on frictionless surface connected by one spring. Natural length of spring is $L$ and force constant $K$. Initially spring is in natural length. Another equivalent block $C$ of mass $m$ travelling at speed $v$ along line joining $A$ & $B$ collide with $A$. In ideal condition maximum compression of spring is :-
Two identical balls $A$ and $B$ are released from the positions shown in figure. They collide elastically on horizontal portion $MN$. The ratio of the heights attained by $A$ and $B$ after collision will be (neglect friction)