A body of mass $2\, kg$ moving with a velocity of $3\, m/sec$ collides head on with a body of mass $1\, kg$ moving in opposite direction with a velocity of $4\, m/sec$. After collision, two bodies stick together and move with a common velocity which in $m/sec$ is equal to

When the momentum of a body increases by $100\%$, its $KE$ increases by .............. $\%$

Work done in time $t$ on a body of mass $m$  which is accelerated from rest to a speed $v$  in time $t_1$  as a function of time $t$  is given by

The force $F$ acting on a body moving in a circle of radius $r$ is always perpendicular to  the instantaneous velocity $v$. The work done by the force on the body in one complete  rotation is : 

A particle of mass $m$ strikes the ground inelastically, with coefficient of restitution $e$

A particle is moved from $(0, 0)$ to $(a, a)$ under a force $\vec F = (3\hat i + 4\hat j)$ from two paths. Path $1$ is $OP$ and path $2$ is $OQP$. Let $W_1$ and $W_2$ be the work done by this force in these two paths respectively. Then