A force $\vec F = (5\hat i + 3\hat j)\;N$is applied over a particle which displaces it from its original position to the point $\vec s = (2\hat i - 1\hat j)$m. The work done on the particle is.........$J$

A particle of mass $m$ moving with velocity $V_0$ strikes a simple pendulum of mass $m$ and sticks to it. The maximum height attained by the pendulum will be

A particle of mass $m$ is moving in a circular path of constant radius $r$ such that its centripetal acceleration $a_c$ is varying with time $t$ as, $a_c = k^2rt^2$, The power delivered to the particle by the forces acting on it is

A ball of mass $M$ falls from a height $h$ on a floor which the coefficient of restitution is $e$. The height attained by the ball after two rebounds is

System shown in figure is released from rest. Pulley and spring are massless and the friction is absent everywhere. The speed of $5\, kg$ block, when $2\, kg$ block leaves the contact with ground is : (take force constant of the spring $K = 40\, N/m$ and $g = 10\, m/s^2$)

A body of mass $m$ is moving in a circle of radius $r$ with a constant speed $v$. The force on the body is $\frac{{m{v^2}}}{r}$ and is directed towards the centre. What is the work done by this force in moving the body over half the circumference of the circle