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Two forces F(1) and F(2) are applied at...

Two forces `F_(1)` and `F_(2)` are applied at the ends of a metal rod of Yougn's Modulus `Y`, length `l` as shown.

Longitudinal stress at the given cross-section `PQ` if the cross-section of the rod is `A_(0)` and tension is `T`

A

`(T sin^(2) theta)/(A_(0))`

B

`(T sin theta)/(A_(0))`

C

`(T sin theta)/(2A_(0))`

D

`(2T sin theta)/(2A_(0))`

Text Solution

Verified by Experts

The correct Answer is:
A

Tension at a distance `x` is given by
`(F_(1) - (F_(1) - F_(2)) (x)/(l))`
Shearing stress `= (T cos theta )/(a// sin theta) = (T sin^(2) theta)/(A_(0))`
where `T = (F_(1) - (F_(1) - F_(2))(x)/(l))`
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