Question

when the momentum of a body increase by 100% its K.E. increases by(kinetic energy)

Answer 1

Let the momentum of the particle be p ,

p = m*v.

where m is the mass of the particle and v is the velocity of the particle.

Now , Kinetic Energy = 1/2 * ( m * v^2 ).

K.E. = 1/2 * ( m^2 *v^2 )/m.

K.E. = 1/2 * ( p^2 )/m.

Now the mass of an object is constant. So the change in momentum is caused by change in velocity .

The momentum is increased by 100 % .

Therefore , the new momentum would be 2*p .

And the new K.E. will be

K.E. = 1/2 * ( 4 * p^2 ) / m. i.e., 4 times the old kinetic energy.

So, the percentage increase in kinetic energy will be 300 % .

Answer 2

keeping the mass of the body as constant...
for the increment of momentum by 100%
new velocity will be 2v
therefore new kinetic energy=½m(v')²
=½m(2v)²
=4[½mv²]
so increment in k.e is 300%