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A uniform chain of length of length pir ...

A uniform chain of length of length `pir` lies inside a smooth semicircular tube (AB) of radius f. Assuming a slight disturbance to start the chain in motion, the velocity it will emerge from the end (B) of the tube will be

A

`sqrt(gr(1+(2)/9pi))`

B

`sqrt(2gr((2)/(pi)+(pi)/2pi))`

C

`sqrt(gr(pi+2))`

D

`sqrt(pigr)`

Text Solution

Verified by Experts

The correct Answer is:
B
`dm=(m/pi)d theta`

`:. dU=(dm)gh=(m/pid theta)gr sin theta`
`U_(i) =int_(0)^(pi)dU =(2mgr)/pi`
Now, `K_(i) +U_(i)=K_(f) + U_(f)`
`:. 0+(2mgr)/pi=1/2mv^(2)-mg((pir)/2)`
`:. v=sqrt(2gr(2/pi + pi/2))`.
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