Question

If kinetic energy of a body is increased by $300\%$ then percentage change in momentum will be

• A. 100%
• B. 150%
• C. 265%
• D. 73.2%

Answer 1

Answer: (A)

Let $m$ be the mass of the body and $v_1$ and $v_2$ be the initial and final velocities of the body respectively.
$\therefore$ Initial kinetic energy $=\frac{1}{2}m{v}_1^2$
Final kinetic energy $=\frac{1}{2}m{v}_2^2$
Initial kinetic energy is increased $300\%$ to get the final kinetic energy.
$\therefore \frac{1}{2}m{v}_2^2=\frac{1}{2}\left(1+\frac{300}{100}\right)m{v}_1^2$
$\Rightarrow v_2=2v_1$
or $v_2/v_1=2$...(i)
Initial momentum $=p_1=m{v}_1$
Final momentum $=p_2=m{v}_2$
$\therefore \frac{p_2}{p_1}=\frac{m{v}_2}{m{v}_1}=\frac{v_2}{v_1}=2$
$\therefore p_2=2p_1=\left(1+\frac{100}{100}\right)p_1$
So momentum has increased $100\%$.