Calculate the recoil velocity of a gun having mass equal to 5 kg, if a bullet of 25 g acquires the velocity of $500m{s}^{-1}$ after firing from the gun.

The correct option is:C: 2.5m/s

Given Data:

mass of bullet, $m_1=25g=0.025kg$

velocity of bullet before firing, $u_1=0{ms}^{-1}$

velocity of bullet after firing, $v_1=500{ms}^{-1}$
mass of gun,$m_2=5kg$
velocity of gun before firing,$u_2=0{ms}^{-1}$
Let velocity of gun after firing be, $v_2$
From law of conservation of momentum,

$m_1{u}_1+m_2{u}_2=m_1{v}_1+m_2{v}_2$

$m_1\times 0+m_2\times 0=0.025\times 500+5\times v_2$

$⟹0=12.5+5v_2$

$⟹v_2=-\frac{12.5}{5}=-2.5m{s}^{-1}$

This means gun moves in opposite direction to bullet, which is called recoil.

Thus, recoil velocity of gun is equal to

${2.5ms}^{-1}$

Here, the negative(- ve) sign shows that gun moves in the opposite direction of bullet.