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 $\sqrt{2}$ = 1.41) (rounding off to nearest integer)

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answer is 3.

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Detailed Solution

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

so potential energy= (mgh)/4

In the inclined position $h' = \frac{3 h}{4} sinθ$

potential energy mgh'=mg $\frac{3 h}{4} sinθ$

given $\frac{m g h}{4} = m g \frac{3 h}{4} \sin θ \sin θ = 1 / 3 r / h = tanθ if sinθ = 1 / 3 tanθ = \frac{1}{2 \sqrt{2}} = r / h h / r = 2 \sqrt{2} = 2.82 \approx 3$

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