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JIPMER 2007
Exam
JIPMER
Year
2007
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

JIPMER 2007 · Physics · Center of Mass, Momentum and Collision

A bomb of mass 30 kg at rest explodes into two pieces of masses 18...

A bomb of mass 30 kg at rest explodes into two pieces of masses 18 kg and 12 kg. The velocity of 18 kg mass is 6 ms−16 \mathrm{~ms}^{-1}. The kinetic energy of the other mass is

Options

  1. A256 J
  2. B486 J
  3. C524 J
  4. D324 J

Correct answer

B. 486 J

Step-by-step solution

The linear momentum of exploding part will remain conserved. Applying conservation of linear momentum, we write, m1u1=m2u2m_1 u_1=m_2 u_2 Here, m1=18 kg,m2=12 kgu1=6 ms−1,u2=?∴18×6=12u2⇒u2=18×612=9 ms−1\begin{gathered}m_1=18 \mathrm{~kg}, m_2=12 \mathrm{~kg} \\ u_1=6 \mathrm{~ms}^{-1}, u_2=?\end{gathered} \therefore 18 \times 6=12 u_2 \Rightarrow u_2=\frac{18 \times 6}{12} = 9 \mathrm{~ms}^{-1} Thus, kinetic energy of 12 kg mass K2=12m1u22=12×12×(9)2=6×81=486 J\begin{aligned} K_2 & =\frac{1}{2} m_1 u_2^2 \\ & =\frac{1}{2} \times 12 \times(9)^2 \\ & =6 \times 81 \\ & =486 \mathrm{~J}\end{aligned}
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