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NEET 2009
Exam
NEET
Year
2009
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

NEET 2009 · Physics · Center of Mass, Momentum and Collision

An explosion blows a rock into three parts. Two parts go off at...

An explosion blows a rock into three parts. Two parts go off at right angles to each other. These two are, 1 kg1 \mathrm{~kg} first part moving with a velocity of 12 ms−112 \mathrm{~ms}^{-1} and 2 kg2 \mathrm{~kg} second part moving with a velocity of 8 ms−18 \mathrm{~ms}^{-1}. If the third part flies off with a velocity of 4 ms−14 \mathrm{~ms}^{-1}, its mass would be

Options

  1. A5 kg5 \mathrm{~kg}
  2. B7 kg7 \mathrm{~kg}
  3. C17 kg17 \mathrm{~kg}
  4. D3 kg3 \mathrm{~kg}

Correct answer

A. 5 kg5 \mathrm{~kg}

Step-by-step solution

Key Idea Apply law of conservation of linear momentum. Momentum of first part =1×12=12kgms−1Momentum=1 \times 12=12 \mathrm{ kg} \mathrm{ ms}^{-1} Momentum of thesecondpart=2×8=16kgms−1the second part =2 \times 8=16 \mathrm{ kg} \mathrm{ ms}^{-1} \thereforeResultantmomentum=(12)2+(16)2=20kgms−1Resultant momentum =\sqrt{(12)^2+(16)^2}=20 \mathrm{ kg} \mathrm{ ms}^{-1} The thirdpartshouldalsohavethesamemomentum.Letthemassofthethirdpartbe,thenthird part should also have the same momentum. Let the mass of the third part be, then4×M=20M=5kg\begin{aligned} 4 \times M & =20 \\ M & =5 \mathrm{ kg} \end{aligned} Alternative : \text{ Alternative : }Mvcos⁡θ=12Mvsin⁡θ=16tan⁡θ=1612=43M=12×54×3=6012=5kg\begin{aligned} \mathrm{Mv} \cos \theta & =12 \\ \mathrm{Mv} \sin \theta & =16 \\ \tan \theta & =\frac{16}{12}=\frac{4}{3} \\ M & =\frac{12 \times 5}{4 \times 3}=\frac{60}{12}=5 \mathrm{ kg} \end{aligned}$$
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