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NEET 2013
Exam
NEET
Year
2013
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

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

An explosion breaks a rock into three parts in a horizontal plane....

An explosion breaks a rock into three parts in a horizontal plane. Two of them go off at right angles to each other. The first part of mass 1 kg1 \mathrm{~kg} moves with a speed of 12 ms−112 \mathrm{~ms}^{-1} and the second part of mass 2 kg2 \mathrm{~kg} moves with 8 ms−18 \mathrm{~ms}^{-1} speed. If the third part flies off with 4 ms−14 \mathrm{~ms}^{-1} speed, then its mass is

Options

  1. A3 kg3 \mathrm{~kg}
  2. B5 kg5 \mathrm{~kg}
  3. C7 kg7 \mathrm{~kg}
  4. D17 kg17 \mathrm{~kg}

Correct answer

B. 5 kg5 \mathrm{~kg}

Step-by-step solution

We have p1+p2+p3=0[∵p=mv]p_1+p_2+p_3=0 [\because p=m v]∴1×12i+2×8j+p3=0⇒12i+16j+p3=0⇒P3=−(12i+16j)∴p3=(12)2+(16)2=144+256=20 kg−m/s\begin{aligned} & \therefore 1 \times 12 i+2 \times 8 j+p_3=0 \\ & \Rightarrow 12 \mathrm{i}+16 \mathrm{j}+\mathrm{p}_3=0 \\ & \Rightarrow \mathrm{P}_3=-(12 \mathrm{i}+16 \mathrm{j}) \\ & \therefore \mathrm{p}_3=\sqrt{(12)^2+(16)^2} \\ & =\sqrt{144+256} \\ & =20 \mathrm{~kg}-\mathrm{m} / \mathrm{s} \end{aligned}$Now,Now,p_3=m_3 v_3 \Rightarrow m_3=\frac{p_3}{V_3}=\frac{20}{4}=5 \mathrm{~kg}$
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