Question

if momentum of the particle is increased by 100%then the%change in kinetic energy will be-​

Answer 1

Answer:

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 v² ).

K.E. = 1/2 × ( m²v² )/m.

K.E. = 1/2 × ( p² )/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 2p .

And the new K.E. will be

K.E. = 1/2 × ( 4p² ) / m.

i.e., 4 times the old kinetic energy.

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