Question

If Kinetic energy increases by 3%. Then momentum will increase by ?

Answer 1

Answer:

Momentum is increased by approximately 1.5%

Explanation:

They're related as

K = p²/(2 m)

From above

p2/p1 = sqrt(K2/K1)

p2/p1 - 1 = sqrt(K2/K1) - 1

∆p = p1 × [sqrt(K2/K1) - 1]

= 100% × [sqrt(103%/100%) - 1]

≈ 1.5%

Answer 2

The momentum will increase by 1.5 %.

Explanation:

The kinetic energy of the body is given as

$K=\frac{1}{2}mv^2$

Here m is the mass and v is the velocity.

The momentum of a body is given as

P = mv

so,

$K = \frac{1}{2m} (mv)^2$

$K=\frac{P^2}{2m}$

Now for small changes,

$\frac{\Delta K}{K} =\frac{2\Delta P}{P}$                   (as mass remains unchanged)

Given $\frac{\Delta K}{K} =3\%$

Substitute the value, we get

$3\% =\frac{2\Delta P}{P}$

$\frac{\Delta P}{P}=\frac{3\%}{2}=1.5\%$

Thus, momentum will increase by 1.5 %.

#Learn More: Kinetic energy, momentum

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