Q.

A solid cone of height ‘h’, radius R and apex angle θ  is placed on a horizontal surface. Its gravitational potential energy is same whether it is placed with its base on the surface or with its curved surface on the horizontal surface. Then h/R=  (take 2 = 1.41) (rounding off to nearest integer)

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answer is 3.

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Detailed Solution

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For solid cone center of mass is at a height h/4 from the base 

so potential energy= (mgh)/4

In the inclined position h'=3h4sinθ

potential energy mgh'=mg3h4sinθ

given mgh4=mg3h4sinθ sinθ=1/3 r/h=tanθ if sinθ=1/3  tanθ=122=r/h h/r=22=2.823

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