Question

A shell of mass 200 g is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is

(a) 40 ms⁻¹

(b) 120 ms⁻¹

(c) 100 ms⁻¹

(d) 10 ms⁻¹

Answer 1

Correct option is : (c) 100 ms⁻¹

Total energy = E₁ + E₂ = 1050 J

As, E \(=\frac{p^2}{2m}\Rightarrow \frac{E_1}{E_2}=\frac{m_2}{m_1}=\frac{4}{0.2}\) = 20.

where, m₁ = mass of shell

and m₂ = mass of gun.

\(\Rightarrow E_2=\frac{E_1}{20}\)

\(\Rightarrow E_1+\frac{E_1}{20}\) = 1050

⇒ E₁ = 1000 J

 ∴ KE = \(\frac{1}{2}m_1v^2_1=1000\)

⇒ v₁ = \(\sqrt{10000}\) = 100 ms^-1