Question

A gun fires a bullet of mass 50 g with a velocity of mass $130$ ms${}^{-1}$. Because of this, the gun is pushed back with a velocity of $1$ ms${}^{-1}$. The mass of the gun is :

• A. 15 kg
• B. 30 kg
• C. 6.5 kg
• D. 20 kg

Answer 1

The correct option is C 6.5 kg

Mass of the gun = $m_1=?$

Mass of the bullet $m_2=50g=0.050kg$

Final velocity of the gun $v_1=-1m/s$ (The minus sign indicates that the gun is pushed back)

Final velocity of the bullet $v_2=130m/s$

Let the system consists of the gun and the bullet. Now the initial momentum is zero.
By using momentum conservation, we get,
$m_1{v}_1+m_2{v}_2=0$
But $v_1=-1$ ms${}^{-1},v_2=130$ms${}^{-1},m_2=\frac{50}{1000}$kg
$\Rightarrow m_1(-1)+\frac{50}{1000}\times 130=0$
$\Rightarrow m_1=6.5$kg