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If the ratio of diameters, lengths and Y...

If the ratio of diameters, lengths and Young’s modulus of steel and copper wires shown in the figure are p, q and s respectively, then the corresponding ratio of increase in their lengths would be

A

`(5q)/((7 sp^(2)))`

B

`(7 q)/((5sp^(2)))`

C

`(2q)/((5sp))`

D

`(7q)/((5sp))`

Text Solution

Verified by Experts

The correct Answer is:
B
`Delta l= (Fl)/(AY)= (Fl)/(pi ((d)/(2))^(2) Y)`
`(Delta l_(1))/(Delta l_(2))= ((l_(1))/(l_(2))) ((d_(2))/(d_(1)))^(2) ((Y_(2))/(Y_(1))) ((F_(1))/(F_(2)))`
`= (7)/(5) xx (q) ((1)/(p))^(2) ((1)/(s))= (7q)/(5 sp^(2))`
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