An inclined plane makes an angle 30 ∘ with the horizontal. A groove OA=5 m cut in the plane makes an angle 30 ∘ with OX. A short smooth cylinder is free to slide down the influence of gravity. Find the time taken by the cylinder to reach from A to O.(Take g = 10 m / s 2 ) A. 1 s B. 2 s C. 3 s D. 4 s

Question

An inclined plane makes an angle       30    ∘   with the horizontal. A groove OA=5 m cut in the plane makes an angle       30    ∘   with OX. A short smooth cylinder is free to slide down the influence of gravity. Find the time taken by the cylinder to reach from A to O.(Take   g  =  10  m      /        s    2  ) A. 1 s B. 2 s C. 3 s D. 4 s

Joanna Sosa · Accepted Answer

The acceleration of gravity acting on the cylinder is due to the inclined plane is   g  sin  ⁡      30    ∘    =      g    2    m      /        s    2  . Now, as the groove is making 30∘ with OX, the acceleration with which the cylinder is sliding down the plane is given by  a  =      g    2    cos  ⁡      60    ∘    =      g    4    m      /        s    2   Now, using equation of motion we get,  s  =  u  t  +      1    2    a      t    2    ⇒  5  =  0  +      1    2    ×      g    4        t    2    ⇒  t  =  2  s  e  c

An inclined plane makes an angle 30 ∘ with the horizontal. A groove OA=5 m...

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