A bullet is fired from a gun with a velocity of 600 m/s. The recoil velocity of the gun is 3 m/s. What is the ratio of the mass of the gun and the bullet? 

A bullet is fired from a gun with a velocity of 600 m/s. The recoil velocity of the gun is 3 m/s. The ratio of the mass of the gun and the bullet is 200:1.

Given,

Initially both Gun and bullet will be at rest ie, the initial velocity of Gun and bullet =0

After fired,

$$\begin{gathered} V_b=600m/s \\ V_r=3m/s \end{gathered}$$

Let the mass of the gun is M and the mass of the bullet be m.

Using momentum conservation:

Initial momentum (Before fired)= Final momentum (After fired)
$M\times 0+m\times 0=(-3\times M)+600\times m$

$0=-3M+600m$

$\Rightarrow {\displaystyle \frac{M}{m}}={\displaystyle \frac{600}{3}}={\displaystyle \frac{200}{1}}$
 

The ratio of the mass of the Gun to the bullet is ${\displaystyle \frac{200}{1}}$.