Two masses m₁ = 4 gm and m₂ = 25 gm are having same kinetic energy, find the ratio of magnitude of their linear momentum.

The correct option is 2 : 5.

Step-by-step Explanation:
Let the mass of the first object be $m_1=4\text{gm}$ and the mass of the second object be $m_2=25\text{gm}$.
Let their respective linear momenta be $p_1$ and $p_2$.

The relationship between kinetic energy ($K$), mass ($m$), and linear momentum ($p$) is given by the formula:
$K=\frac{p^2}{2m}$

Solving for linear momentum $p$, we get:
$p=\sqrt{2mK}$

Since both masses have the same kinetic energy ($K_1=K_2=K$), we can write the ratio of their momenta as:
$\frac{p_1}{p_2}=\frac{\sqrt{2m_{1}K}}{\sqrt{2m_{2}K}}$

Simplifying the ratio by cancelling out common terms:
$\frac{p_1}{p_2}=\sqrt{\frac{m_1}{m_2}}$

Substitute the given values of $m_1$ and $m_2$ into the equation:
$\frac{p_1}{p_2}=\sqrt{\frac{4}{25}}$

Calculating the square roots:
$\frac{p_1}{p_2}=\frac{2}{5}$

Thus, the ratio of the magnitude of their linear momentum is 2 : 5.