A skier plans to ski a smooth fixed hemisphere of radius R . He starts from rest from a curved smooth surface of height $> (\frac{R}{4})$ . The angle $θ$ at which he leaves the hemisphere is $cos^{- 1} (x)$ . Find $x$ .

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At the time of leaving contact, N = 0 ∴ m g cos θ = R mv 2 ​ = R m ( 2 gh ) ​ ∴ cos θ = R 2 h ​ = R 2 [ 4 R ​ − R ( 1 − c o s θ ) ] ​ On solving this equation, we get, cos θ = 5/6 ⇒ θ = cos − 1 ( 6 5 ​ ) = cos − 1 ( 0.83 )

Physics - Circular Motion Question with Solution | TestHub

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