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Laws Of Motion

Question
CBSEENPH11020753

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

  • 100 ms-1

  • 80 ms-1

  • 40 ms-1

  • 120 ms-1

Solution

A.

100 ms-1

In the given problem conservation of linear momentum and energy hold good.
Conservation of momentum yields.
m1v1 + m2v2 = 0
4v1 + 0.2 v2  = 0
Conservation of energy yields

1 half straight m subscript 1 straight v subscript 1 squared space plus 1 half space straight m subscript 2 straight v subscript 2 squared space equals space 1050 space space space... left parenthesis straight i right parenthesis
or
1 half space straight x 4 straight v subscript 1 squared space plus space 1 half 0.1 straight v subscript 2 squared space equals space 1050 space space space.... space left parenthesis ii right parenthesis

solving space eqs. space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis space we space have
straight v subscript 1 space equals space 100 space straight m divided by straight s