Physics-
General
Easy

Question

A thin uniform rod of mass M and length L hangs from a frictionless pivot and is connected at the bottom by a spring to the wall as shown. The spring constant is K. The system is allowed to oscillate by pressing end B of the rod and releasing. The period of oscillation will be

  1. T equals 2 pi square root of fraction numerator M over denominator K end fraction end root    
  2. T equals 2 pi square root of fraction numerator M L over denominator M g plus K L end fraction end root    
  3. T equals 2 pi square root of fraction numerator 2 M L over denominator 6 K L plus 3 M g end fraction end root    
  4. T equals 2 pi square root of fraction numerator M L over denominator 3 K L plus 2 M g end fraction end root    

The correct answer is: T equals 2 pi square root of fraction numerator 2 M L over denominator 6 K L plus 3 M g end fraction end root


    k x cross times l plus m g sin invisible function application theta fraction numerator l over denominator 2 end fraction equals fraction numerator m l to the power of 2 end exponent over denominator 3 end fraction alpha
    If theta is small rightwards arrow x equals l theta comma sin invisible function application theta equals theta

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