Question

If the kinetic energy of a body becomes four times of its initial value, then new momentum will

• A. become four times, its initial value
• B. become three times, its initial value
• C. become twice its initial value
• D. ramains constant

Answer 1

Answer: (C)

become twice its initial value

Answer 2

The kinetic energy of a body of mass $m$ and velocity $v$ is $E=\frac{1}{2} m v^{2}=\frac{p^{2}}{2 m}$ where $p=m v=$ momentum of the body $\therefore \frac{p^{2}}{E}=2 m=$ constant $\because m=$ constant $\frac{p_{1}^{2}}{E_{ l }}=\frac{p_{2}^{2}}{E_{2}}$ Now, $E_{2}=4 E_{1}$ $\therefore \frac{p_{1}^{2}}{p_{2}^{2}}=\frac{1}{4}$ $\Rightarrow \frac{p_{1}}{p_{2}}=\frac{1}{2} \Rightarrow p_{2}=2 p_{1}$