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A steel wire is suspended vertically fro...

A steel wire is suspended vertically from a rigid support. When loaded with a weight in air, it expands by `L_(a)` and when the weight is immersed completely in water, the extension is reduced to `L_(w)`. Then relative density of the material of weight is

A

`(l_(a))/(l_(w))`

B

`(l_(a))/(l_(a)-l_(w))`

C

`(l_(w))/(l_(a)-l_(w))`

D

`(l_(w))/(l_(a))`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `W_(a)andW_(w)` be weight and apparent weight
Now `l_(a)=(W_(a)L)/(Agamma)`
and `l_(W)=(W_(w)L)/(Agamma)rArr(W_(w))/(W_(a))=(l_(w))/(l_(a))`
where `W_(W)=W_(a)-B`
`=W_(a)-Vrhog`
`=W_(a)-(W_(a))/(d)rho=W_(a)(1-(rho)/(d))`
(i) `rArrW_(omega)=W_(a)(l_(w))/(l_(a))=W_(a)(1-(rho)/d)rArr(d)/(rho)=(l_(a))/(l_(a)-l_(w))`
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