Practice question

Given: A shell of mass 0.01 kg is fired from a gun of mass 50 kg with a muzzle speed of 100 m/s . What is the recoil speed of the gun? These values define the system as per NCERT data. Formula: Before firing: p_{initial = 0. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: By conservation of momentum, total momentum before and after firing is zero. . After firing: m_{shell v_{shell + m_{gun v_{gun = 0 . Substitute: 0.01 × 100 + 50 × v_{gun = 0 . 1 + 50 v_{gun = 0 Rightarrow v_{gun = -1/50 = -0.02 m/s . Recoil speed (magnitude) = 0.02 m/s . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.