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KVPY2017PhysicsOscillations

One end of a rod of length L is fixed to a point on the circumference of a wheel of radius R . The other end is sliding freely along a straight channel passing through the centre O of the wheel as shown in the figure below. The wheel is rotating with a constant angular velocity about O . Taking T = 2 the motion of the rod is

Options

  1. Asimple harmonic with a period of T
  2. Bsimple harmonic with a period of T / 2
  3. Cnot simple harmonic but periodic with a period of T
  4. Dnot simple harmonic but periodic with a period of T / 2

Correct answer

C. not simple harmonic but periodic with a period of T

Step-by-step solution

array l = R ²+ x ²- L ² 2 Rx x ²=2 Rx cosec + L ²- R ² array displacement of S.H. M. is in the form of x = A t + c Therefore it is not S. H. M. It is S. H. M. only which. It L = R . array l x ²=2 Rx x =2 R x =2 R t [ S.H. M.] array But period of this motion is T

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