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A uniform elastic rod of cross section a...


A uniform elastic rod of cross section area A natural length L and Young's modulus Y is placed on a smooth horizontal surface. Now two horizontal forces (of magnitude F and 3F) directed along the length of rod and in opposite direction act at two of its ends as shown . After the rod has acquired steady state, the extension of the rod will be

A

`(2F)/(YA)L`

B

`(4F)/(YA)L`

C

`(F)/(YA)L`

D

`(3F)/(2YA) L`

Text Solution

Verified by Experts

The correct Answer is:
A

Tension in rod at a distance x from right edge is
`T_F(3- (2x)/(L))`
`therefore` Net extension in rod `=underset(0)overset(pi)int (T)/(4A) dx=(2F)/(YA) L`
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