Question

If linear momentum of abody is increased by 20 % what will be the % increase in the kinetic energy of the body

Answer 1

Answer:

Kinetic energy is increased by 44%.

Explanation:

Linear momentum(p) = mv

Kinetic Energy(K) = 1/2 mv² or mv²/2

Linear momentum is increased by 20%.

Linear momentum is directly proportional to velocity, (considering mass of the Body be constant).

So, 20% increase in momentum means 20% increase in Velocity.

Now new velocity, v' = v + 20% of v

v' = ( 1 + 20% ) of v

= (1 + (20/100)) × v

v' = 1.2v ___________(1)

Now, new kinetic energy, K' = mv'²/2

K' = (m (1.2v)²)/2 = (1.44mv²)/2

So, increase in Kinetic energy= K' - K

= 1.44mv²/2 - mv²/2 = 0.44

Percentage increase = [((K'-K)/K)*100]%

= [(0.44/1)*100]%

= 44%