'A' is a huge planet with uniform mass distribution, mass M, radius R. B is a circular tunnel made in it, concentric with planet. Radius of tunnel is r, ( r = 2 R ) cross sectional diamete

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'A' is a huge planet with uniform mass distribution, mass M, radius R. B is a circular tunnel made in it, concentric with planet. Radius of tunnel is r, $(r = \frac{R}{2}$ ) cross sectional diameter is d (d << r). C is a small ball of mass $m (m ≪ M)$ which is moving freely inside the tunnel without friction in a uniform circular motion, take acceleration due to gravity on surface of A as g :-

TestHub · Accepted Answer

For contact force = 2 field free ​ N + mg ′ = mr ω 2 2 mg ′ + mg ′ = mr ω 2 3 g ′ = r ω 2 3 g ( R r ​ ) = r 2 ​ ω = R 3 g ​ ​ for N = 0 , ​ g ′ = mr ω 2 g R r ​ = mr ω 2 ​ ω = independent of r

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