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A uniform chain of mass m and length l h...

A uniform chain of mass `m` and length `l` hangs on a thread and touches the surface of a table by its lower end. Thread breaks suddenly. Find the force exerted by the table on the chain when half of its length has fallen on the table. The fallen part does not form heap

A

`3/2mg`

B

`mg`

C

`0`

D

`5/2mg`

Text Solution

Verified by Experts

The correct Answer is:
A
Force exerted by the chain on the table consists of two parts:

1. Weight of the portion BC of the chain lying on the table,
`W=(mg)/(2)` (downwards)
2. Thrust force `F_t=lambdav^2`
Here, `lambda="mass per unit length of chain" =m/l`
`v^2=(sqrt(gl))^2=gl`
`:. F_t=(m/l)(gl)=mg` (downwards)
`:.` Net force exerted by the chain on the table is
`F=W+F_t=(mg)/(2)+mg=3/2mg` (downwards)
So, from Newton's third law the force exerted by the table on the chain will be `3/2mg`(vertically upwards).
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