Two bodies are having kinetic energies in the ratio $$16 : 9$$. If they have same linear momentum, the ratio of their masses respectively is:

Kinetic energy in terms of momentum: $$K = \frac{p^2}{2m}$$

Since both bodies have the same linear momentum $$p$$:

$$K_1 = \frac{p^2}{2m_1}$$ and $$K_2 = \frac{p^2}{2m_2}$$

Taking the ratio:

$$\frac{K_1}{K_2} = \frac{m_2}{m_1}$$

Given $$\frac{K_1}{K_2} = \frac{16}{9}$$:

$$\frac{m_2}{m_1} = \frac{16}{9}$$

$$\frac{m_1}{m_2} = \frac{9}{16}$$

The ratio of their masses is $$\mathbf{9 : 16}$$.

Predict your JEE Main percentile, rank & performance in seconds

Check Your Score Now

Ask our AI anything

AI can make mistakes. Please verify important information.

Download resources