Question

A particle is moving in translatory motion. If momentum of the particle decreases by $10$%, kinetic energy will decrease by :

• A. $10$%
• B. $5$%
• C. $20$%
• D. $19$%

Answer 1

The correct option is D $19$%

According to question,
Momentum of the particle decrease by $10$%.
As we know, momentum of particle
$p=\sqrt{2mK}$
$\Rightarrow p\propto \sqrt{K}$ and $p_1\propto \sqrt{K_1}$
Final momentum, $p_1=p-\frac{10p}{100}$
$\Rightarrow p_1=\frac{90p}{100}$
So, $\frac{p}{p_1}=\sqrt{\frac{K}{K_1}}\Rightarrow {\left(\frac{100}{90}\right)}^2=\frac{K}{K_1}$
$\Rightarrow \frac{10000}{8100}=\frac{K}{K_1}$
$\Rightarrow \frac{81}{100}=\frac{K_1}{K}$
Decreasing both sides from $1$,
$1-\frac{81}{100}=1-\frac{K_1}{K}$
$\Rightarrow \frac{100-81}{100}=\frac{K-K_1}{K}$
$\frac{K-K_1}{K}=\frac{19}{100}$
Change in kinetic energy
$\Rightarrow \left(\frac{K-K_1}{K}\right)\times 100=\left(\frac{19}{100}\right)\times 100=19$%