Question

If Kinetic energy of body increases by $300\%$, What will be $\%$age of linear momentum?

Answer 1

The momentum increases by $100\%$
Let initial kinetic energy be K and momentum be p.
$K=\frac{1}{2}m{v}^2\left(Equation1\right)$
If K increases by 300%, it increases by a factor of $\frac{300\%}{100\%}=3$
So the new kinetic energy is
K’ = K + 3K = 4K
From Equation 1: $v=\sqrt{\frac{2K}{m}}$
The initial momentum $p=mv=m\times \sqrt{\frac{2k}{m}\sqrt{m^2\times \frac{2x}{m}}}=\sqrt{2Km}$
The new momentum $p^{\prime }=\sqrt{2K^{\prime }m}$
$So\frac{p^{\prime }}{p}=\sqrt{\frac{2K^{\prime }m}{2Km}}$
$\frac{p^{\prime }}{p}=\sqrt{\frac{k^{\prime }}{k}}$
$\frac{p^{\prime }}{p}=\sqrt{\frac{4k}{k}}$
$\frac{p^{\prime }}{p}=2$
p' = 2p
$\%change=\frac{p^{\prime }-p}{p}\times 100\%=\frac{2p-p}{p}\times 100\%=100\%$
$\%$ increase in momentum $=100\%$