Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NEET 2013
Exam
NEET
Year
2013
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

NEET 2013 · Physics · Center of Mass, Momentum and Collision

A person holding a rifle (mass of person and rifle together is 100...

A person holding a rifle (mass of person and rifle together is 100 kg100 \mathrm{~kg} ) stands on a smooth surface and fires 10 shots horizontally, in 5 s5 \mathrm{~s}. Each bullet has a mass of 10 g10 \mathrm{~g} with a muzzle velocity of 800 ms−1800 \mathrm{~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-0.08 \mathrm{~ms}^{-1}, 16 \mathrm{~N}
  2. B−0.08 ms−1,16 N-0.08 \mathrm{~ms}^{-1}, 16 \mathrm{~N}
  3. C−0.08 ms−1,16 N-0.08 \mathrm{~ms}^{-1}, 16 \mathrm{~N}
  4. D−0.08 ms−1,16 N-0.08 \mathrm{~ms}^{-1}, 16 \mathrm{~N}

Correct answer

B. −0.08 ms−1,16 N-0.08 \mathrm{~ms}^{-1}, 16 \mathrm{~N}

Step-by-step solution

Using law of conservation of moments Initial momentum =mu1+mu2final momentum =nmv1+(M−nm)v2∴mu1+mu2=nmv1+(M−nm)v20=10×101000×800+(100−10×101000)r2\begin{aligned} & \text{Initial momentum }=m u_1+m u_2 \\ & \text{final momentum }=n m v_1+ \\ & (M-n m) v_2 \\ & \therefore m u_1+m u_2=n m v_1+(M-n m) v_2 \\ & 0=\frac{10 \times 10}{1000} \times 800 +\left(100-\frac{10 \times 10}{1000}\right) r^2 \end{aligned}−80=99910v2⇒v2=−0.8ms−1\begin{aligned} -80 & =\frac{999}{10} v_2 \\ \Rightarrow v_2 & =-0.8 \mathrm{ ms}^{-1} \end{aligned}AndaverageforceexertedonthepersonAnd average force exerted on the person=n×m×uΔt=n×m×uΔt=10×1G1000×8005=805=16N\begin{array}{l} =\frac{n \times m \times u}{\Delta t} \\ =\frac{n \times m \times u}{\Delta t} \\ =\frac{10 \times \frac{1 \mathrm{G}}{1000} \times 800}{5} \\ =\frac{80}{5}=16 \mathrm{ N} \end{array}$
Practice Center of Mass, Momentum and Collision on Quantrex Academy →

More from Center of Mass, Momentum and Collision

A frictionless circular wire of unit radius is fixed on the horizontal plane. Two point… NEET 2026Bob B of mass m at rest is hanging vertically from the ceiling via a massless string of… NEET 2026A ball of mass 0.5 kg is dropped from a height of 40 m . The ball hits the ground and… NEET 2025Two bodies A and B of same mass undergo completely inelastic one dimensional collision.… NEET 2024Two particles A and B initially at rest, move towards each other under mutual force of… NEET 2023A 1 ~kg object strikes a wall with velocity 1 ~ms^ -1 at an angle of 60^ ∘ with the wall… NEET 2023A bullet of mass m hits a block of mass M elastically. The transfer of energy is the… NEET 2023A shell of mass m is at rest initially. It explodes into three fragments having mass in… NEET 2022 Full Center of Mass, Momentum and Collision list All NEET PYQs