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If the ratio of lengths, radii and young...

If the ratio of lengths, radii and young's modulii of steel and brass wires in the figure are a,b and c, respectively. Then, the corresponding ratio of increase in their lengths would be

A

`(2cm)/(b^(2))`

B

`(3a)/(2b^(2)c)`

C

`(3c)/(2ab^(2))`

D

`(2a^(2)c)/(b)`

Text Solution

Verified by Experts

The correct Answer is:
B
Young's modulus is given by
`Y=(Fl)/(A Deltal)`
`thereforeDeltal=(Fl)/(AY),(Deltal_(S))/(Deltal_(B))`
`=(F_(S))/(F_(B))xx(l_(S))/(l_(B))xx(A_(B))/(A_(S))xx(Y_(B))/(Y_(S))`
or `(Deltal_(S))/(Deltal_(B))=((3mg)/(2mg))xxaxx(1)/(b^(2))xx(1)/(c)=(3a)/(2b^(2)c)`
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