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Question

A uniform chain of length πr lies inside a smooth semicircular tube AB of radius r. Assuming a slightly disturbance to start the chain in motion, the velocity with which it will emerge from the end B of tube will be:
117427.png

A
gr(1+2π)
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B
2gr(2π+π2)
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C
gr(π+2)
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D
πgr
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Solution

The correct option is B 2gr(2π+π2)
dm=(mπ)dθ

dU=(dm)gh=(mπdθ)grsinθ

Ui=π0dU=2mgrπ

Now, Ki+Ui=Kf+Uf

0+2mgrπ=12mv2mg(πr2)

v=2gr(2π+π2)

133305_117427_ans.png

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