Question

A gun of mass M fires a shell of mass 1.5 kg with
a velocity of 150 m/s and recoils with a velocity of
1.5 m/s.Calculate the mass of the gun.​

Answer 1

We have,

Mass of gun = (M) kg $(m_a)$

Mass of shell = 1.5 kg $(m_b)$

Initial velocity of gun and shell = 0 m/s (rest) $(u_a / u_b)$

Recoil velocity (final) of gun = 1.5 m/s $(v_a)$

Final velocity of shell = 150 m/s $(v_b)$

(Assume that there is no external unbalanced force acting in the system.)

According to the law of conservation of Momentum,

${ \star \ \boxed{{m_a u_a + m_b u_b = m_a v_a + m_b v_b}}}$

LHS:-

M(0 m/s) + 1.5 kg(0 m/s)

= 0 kg m/s

RHS:-

M(- 1.5 m/s) + (1.5 kg)(150 m/s)

= (- 1.5M + 225) kg m/s

∵ LHS = RHS,

(- 1.5 M + 225) = 0

⇒ - 1.5M = - 225

⇒ 1.5M = 225

⇒ M = 150 kg (answer).