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A uniform elastic plank moves due to a ...

A uniform elastic plank moves due to a constant force `F_(0)` applied at one end whose area is `S`. The Young's modulus of the plank is `Y`. The strain produced in the direction of force is

A

`(F)/(SE)`

B

`(F)/(2SE)`

C

`(F)/(4SE)`

D

Zero

Text Solution

Verified by Experts

The correct Answer is:
B
(b) Tension at distance x from end `A, T_(x)=F-(F)/(L)x`

Total change in length , `Deltal=int_(0)^(L)(Txdx)/(ES)=(FL)/(2FS)`
`therefore` Average strain `=(Deltal)/(L)=(F)/(2ES)`
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