The kinetic energy of two masses m1 and m2 are equal. The ratio of their linear momentum will be

The correct option is $\sqrt{\frac{m_1}{m_2}}$.

To find the ratio of the linear momentum of two masses, let us establish the relationship between kinetic energy (K) and linear momentum (p).
The linear momentum of an object of mass m moving with velocity v is given by the formula:
$p=mv$

The kinetic energy (K) of the same object is given by:
$K=\frac{1}{2}m{v}^2$

We can rewrite the kinetic energy formula in terms of momentum by multiplying the numerator and denominator by m:
$K=\frac{m^2{v}^2}{2m}=\frac{p^2}{2m}$

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

Let the two masses be $m_1$ and $m_2$, and their respective linear momenta be $p_1$ and $p_2$. Since their kinetic energies are equal, we can denote the common kinetic energy as K:
$p_1=\sqrt{2m_{1}K}$
$p_2=\sqrt{2m_{2}K}$

Now, we find the ratio of their linear momenta:
$\frac{p_1}{p_2}=\frac{\sqrt{2m_{1}K}}{\sqrt{2m_{2}K}}$

Simplifying the fraction by cancelling the common terms (2 and K) under the square root, we obtain:
$\frac{p_1}{p_2}=\sqrt{\frac{m_1}{m_2}}$

Therefore, the ratio of their linear momentum is $\sqrt{\frac{m_1}{m_2}}$ (or $\sqrt{m_1}/\sqrt{m_2}$).