Question

Two bodies of mass 4 g and 25 g are moving with equal kinetic energies. The ratio of the magnitude of their linear momentum is:

• A. 3:5
• B. 2:5
• C. 5:4
• D. 4:5

Answer 1

Answer: (B)

2:5

Answer 2

For objects with equal kinetic energies $\left(\frac{p_1^2}{2m_1} = \frac{p_2^2}{2m_2}\right)$, we have:

$\frac{p_1}{p_2} = \sqrt{\frac{m_1}{m_2}}$

Substituting $m_1 = 4 \, \text{g}$ and $m_2 = 25 \, \text{g}$:

$\frac{p_1}{p_2} = \sqrt{\frac{4}{25}} = \frac{2}{5}$

Thus, the ratio of their momenta is 2 : 5.