Question

When the momentum is decreases by 10% then the kinetic energy is decresed by?

Answer 1

Let the initial momentum and final momentum be mv1mv1 and mv2mv2 respectively.

Let the initial kinetic energy and final kinetic energy be 12mv2112mv12 and 12mv2212mv22 respectively.

It is given that the momentum decreases by 10%.10%.

⇒mv2mv1=0.91=0.9.⇒mv2mv1=0.91=0.9.

⇒v2v1=0.9⇒v22v21=0.81.⇒v2v1=0.9⇒v22v12=0.81.

The ratio of the kinetic energies is 12mv2212mv21=v22v21=0.81.12mv2212mv12=v22v12=0.81.

⇒⇒ The kinetic energy reduces by 19%.