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NEET2013PhysicsCenter of Mass, Momentum and CollisionActual

A person holding a rifle (mass of person and rifle together is 100 ~kg ) stands on a smooth surface and fires 10 shots horizontally, in 5 ~s . Each bullet has a mass of 10 ~g with a muzzle velocity of 800 ~ms ⁻¹ . The final velocity acquired by the person and the average force exerted on the person are:

Options

  1. A-0.08 ~ms ⁻¹, 16 ~N
  2. B-0.08 ~ms ⁻¹, 16 ~N
  3. C-0.08 ~ms ⁻¹, 16 ~N
  4. D-0.08 ~ms ⁻¹, 16 ~N

Correct answer

B. -0.08 ~ms ⁻¹, 16 ~N

Step-by-step solution

Using law of conservation of moments aligned & Initial momentum =m u₁+m u₂ & final momentum =n m v₁+ & (M-n m) v₂ & m u₁+m u₂=n m v₁+(M-n m) v₂ & 0= 10 10 1000 800 + (100- 10 10 1000 ) r^2 aligned aligned -80 & = 999 10 v₂ v₂ & =-0.8 ~ms ⁻¹ aligned And average force exerted on the person array l = n m u t = n m u t = 10 1 G 1000 800 5 = 80 5 =16 ~N array

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