Question

A bullet of $5$ g is fired from a pistol of $1.5$ kg. If the recoil velocity of pistol is $1.5$ $\frac{m}{s}$, find the velocity of bullet. (in $\frac{m}{s}$)

• A. 450 m/s
• B. $400$ $\frac{m}{s}$
• C. $500$ $\frac{m}{s}$
• D. $600$ $\frac{m}{s}$

Answer 1

The correct option is A

450 m/s

Here, we have,

Mass of bullet, $m_1=5$ g $=\frac{5}{1000}$ kg $=0.005$ kg

Mass of pistol, $m_2=1.5$ kg

Recoil velocity of pistol \(v_2 = 1.5\) m/s

We have to find the velocity of the bullet, $v_1$.

Since, before firing, the bullet and pistol are in rest, thus

Initial velocity of bullet, $u_1=0$

And initial recoil velocity of pistol, $u_2=0$

We know that,

\(m_1 u_1+m_2 ​​u_2​​​​​​​ = m_1 v_1​​​​​​​+m_2 v_2\)​​​​​​​

$\Rightarrow 0.005\times 0+1.5\times 0=0.005\times v_1+1.5\times 1.5$ $\frac{m}{s}$)

$\Rightarrow 0=0.005\times v_1+2.25$ $kg\frac{m}{s}$

$\Rightarrow 0.005\times v_1=-2.25$ $kg\frac{m}{s}$

$\Rightarrow v_1=\frac{-2.25}{0.005}=-450$ $\frac{m}{s}$

Thus, the velocity of bullet $=450$ $\frac{m}{s}$, here negative sign shows that, bullet moves in the opposite direction of recoiling of the gun.