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QAIPMT-2008-Ph-2275: NEET 2008 Physics - Class 11 AIPMT-2008-Ph-2275 Solution: A shell of mass 200 gm is ejected from a gun of mass 4 kg by an …

A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1.05 kJ of energy. The initial velocity of the shell is:

Multiple Choice Options

  • A 40 ms−140\ \text{ms}^{-1}
  • B 120 ms−1120\ \text{ms}^{-1}
  • C 100 ms−1100\ \text{ms}^{-1}
  • D 80 ms−180\ \text{ms}^{-1}

Step-by-Step Verified Solution

As per laws of conservation of momentum and energy, if v and V represents initial velocity of shell of mass m and recoil velocity of gun of mass M respectively, then mv + MV = 0 V = _ ( m M ) v = _ ( 0.2 4 ) v = _ v 20 m / s Here (�) sign shows that recoil velocity of gun is opposite to velocity of shell. The energy of explosion is used to impart kinetic energy to shell and gun so that we have 1 2 (mv 2 + MV 2 ) = 1.05 _ 10 3 1 2 [0.2v 2 + (4v 2 / 400)] = 1.05 _10 3 _ v 2 = 10 4 _ v = 100 m/s

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