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text  A linear impulse  end text integral F d t text  acts at a point  end text straight C text  of the smooth  end text rod invisible function application AB text  . The value of  end text straight x text  is so that the end  end text
A space r e m a i n s space s t a t i o n a r y space j u s t space a f t e r space t h e space i m p a c t space i s space colon

  1. iota over 4
  2. iota over 3
  3. iota over 6
  4. iota over 5

The correct answer is: iota over 6


    text  Let  end text straight J text  be the impulse acting on the rod  end text J equals m v subscript c m end subscript semicolon J x equals 1 over 12 straight m l squared omega text  . since the end  end text straight A text  is stationary  end text
V subscript A equals V subscript c m end subscript minus l over 2 omega equals J over m minus open parentheses fraction numerator 12 J x over denominator m l squared end fraction close parentheses l over 2 equals 0

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