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.........$J$

In an elastic collision of two particles the following quantity is conserved

The potential energy of a diatomic molecule is given by $U = \frac{A}{{{r^{12}}}} - \frac{B}{{{r^6}}}$ . $A$ and $B$ are positive constants. The distance $r$ between them at equilibrium is 

A neutron makes a head-on elastic collision with a stationary deuteron. The fractional energy loss of the neutron in the collision is

A body of mass $m$ is moving in a circle of radius $r$ with a constant speed $u$. The force on the body is $mv^2/r$ 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?

Consider two carts, of masses $m$ and $2m$ , at rest on an air track. If you push both the carts for $3\,s$ exerting equal force on each, the kinetic energy of the light cart is