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A particle rest on the top of a smooth hemisphere of radius r. It is imparted a horizontal velocity of √(ngr) (root). The angle made by radius vector joining the particle with the verticle, at the instant, the particle looses contact with sphere is Θ. Find cosΘ.

A particle rest on the top of a smooth hemisphere of radius r. It is imparted a horizontal velocity of √(ngr) (root). The angle made by radius vector joining the particle with the verticle, at the instant, the particle looses contact with sphere is Θ.


Find cosΘ.

Grade:12

1 Answers

vikas askiitian expert
509 Points
11 years ago

      applying energy conservatin

1/2mu^2 +mgr(1-cosq)=1/2mv^2   eq-1

       u^2=ngr           (given)

and we have

                  mgcosq-N=(mv^2)/r    eq-2

  here N  normal reaction ,at this point N is zero

on solving we get

                     cosq=(n+2)/4

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