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Asked by rajv02176 | 12 Sep, 2020, 05:01: AM
Let h be the height or radius of hemisphere. Initially the centre of mass of chain is at a height  ( h sin75 ) as shown in figure.

If chain is falling along the hemispherical surface , centre of mass of chain is at a height ( h sin15 ) when the chain just hit the ground.

Hence potential energy difference due to height difference ( h sin75 - h sin15 ) is converted to kineteic energy

v2 = 2 g h ( sin75 - sin 15 ) = 13.86 h ................. (1)

length of chain = h × ( π / 6)

mass of chain m = λ × h × ( π / 6) ....................(2)

where λ is linear mass density , i.e. mass per unit length of chain

Let us substitute h from eqn.(2)  and rewrite eqn.(1) as  ,   v2 = 13.86 × [ 6 m / ( λ π ) ]  = 26.5 ( m / λ )

Hence speed of chain v = 5.14 ( m / λ )1/2
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