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Torque about a Point

A cylindrical...

Question

A cylindrical uniform rod of the area of cross-section A is acted upon by two forces (each F) as shown. The shearing stress on the section xy is

A

\frac{F s i n 2 θ}{A}

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B

\frac{F s i n 2 θ}{2 A}

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C

\frac{F c o s^{2} θ}{A}

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D

\frac{F s i n^{2} θ}{A}

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Solution

The correct option is B $\frac{F s i n 2 θ}{2 A}$
$S h e a r s t r e s s = \frac{T a n g e n t i a l f o r c e}{A r e a} = \frac{F s i n θ}{\frac{A}{c o s θ}} = \frac{F s i n θ c o s θ}{A} = \frac{F s i n 2 θ}{2 A}$

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Torque about a Point

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