Question

if kinetic energy of a body increases by 100% by what percent will its Momentum increase

Answer 1

To answer this question we must decide how the kinetic energy is being changed.  Kinetic energy depends on both the mass and the speed of the object in question.  We can change the kinetic energy by changing either the one or the other, or both.  To simplify the answer we will assume we will change either the mass or the speed, but not both.

To double the kinetic energy (which in other words means changing the K.E. by 100%) by changing the mass we look at the the equation for KE and see that it is directly proportional to the mass:
$KE = \frac{1}{2} m {v}^{2} = \frac{p}{2m}$
Examination of the momentum equation shows that it too is directly proportional to the mass:
$p = mv$
therefore, doubling the kinetic energy by doubling the mass will also double the momentum. Or in other words change the momentum by 100%.

If we double the kinetic energy by changing the speed, we notice that because KE is proportional to:
${v}^{2}$
to double the KE we must increase the velocity by a factor of √2.

Because momentum is directly proportional to the speed as well as mass, doubling the kinetic energy by changing the speed will increase the momentum by a factor √2, or make it √2  times larger. Which in other words means change it by 41.4%.

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Answer 2

Answer: 41.4%

Explanation:

Let final KE = KE'

Then,

KE' = KE + 100/100 KE

= 2 KE

= 2 * 1/2 MV^ 2

= 2 MV^2

1/2 MV'^2 = 2 MV^2

Therefore V' = 2V....... (1)

Now,

Momentum(p) = MV

Let new Momentum be MV'

Therefore, MV' = M(2 V)

= 2 MV

Now u can easily derive the percentage values carrying forward