91Ó°ÊÓ

Kinetic Energy

$\mathit{K}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathit{m}{\mathit{v}}^{\mathbf{2}}$

Momentum

$\stackrel{\mathbf{→}}{\mathbf{p}}\mathbf{=}\mathit{m}\stackrel{\mathbf{→}}{\mathbf{v}}$

From the formula of the momentum, we can conclude that if the momentum of a single object is zero it implies that the velocity of that object is zero because the mass of an object cannot be zero.

Since the kinetic energy of an object depends on its velocity, if velocity is zero then kinetic energy is also zero.

Hence, we can conclude that if the momentum of a single object is zero then its kinetic energy isalso zero.

The momentum of an object is a vector quantity so if the momentum of a pair of objects is zero then two objects may be having velocities equal in magnitude but different in direction. So total momentum adds up to zero.

But kinetic energy of an object is scaler quantity which does not depend on the direction of velocity so in this case, kinetic energy will not be zero.

Hence, we can conclude that if the momentum of a pair of objects is zero then the kinetic energy of pair of objects doesn't need to be also zero.

Sincekinetic energy is a scalar quantity, so if the kinetic energy of pair of objects is zero, it implies that the velocity of each object is zero because the mass of an object cannot be zero.

Since the momentum depends onvelocity, if velocity is zero then momentum is also zero.

Hence, we can conclude that if the kinetic energy of pair of objects is zero then momentum also is zero.