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Byju's Answer

Standard XII

Physics

Shear Modulus

A bar of cros...

Question

A bar of cross-section A is subjected to equal and opposite tensile forces at its ends. Consider a plane section of the bar whose normal makes an angle $θ$ with the axis of the bar.
What is the shearing stress on this plane?

Shearing stress =

\frac{F}{2 A} s i n 2 θ

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Shearing stress =

\frac{F}{2 A} s i n 3 θ

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Shearing stress =

\frac{F}{2 A} s i n 4 θ

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Shearing stress =

\frac{F}{2 A} s i n θ

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Solution

The correct option is A Shearing stress = $\frac{F}{2 A} s i n 2 θ$

Shearing stress $= \frac{f o r c e}{a r e a}$
Shearing stress applied on the top face
So, $F = F sin θ$
Area of plane section perpendicular to the force $= A sec θ$
Shearing stress $= \frac{F sin θ}{A sec θ}$
$= \frac{2. F sin θ cos θ}{2. A}$
$= \frac{F (2 sin θ cos θ)}{2 A}$
$= \frac{F}{2 A} sin 2 θ$

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A bar of cross-section A is subjected to equal and opposite tensile forces at its ends. Consider a plane section of the bar whose normal makes an angle θ with the axis of the bar.What is the shearing stress on this plane?

The correct option is A Shearing stress = F2Asin2θ Shearing stress=forceareaShearing stress applied on the top faceSo, F=FsinθArea of plane section perpendicular to the force =AsecθShearing stress=FsinθAsecθ=2.Fsinθcosθ2.A=F(2sinθcosθ)2A=F2Asin2θ

A bar of cross-section A is subjected to equal and opposite tensile forces at its ends. Consider a plane section of the bar whose normal makes an angle $θ$ with the axis of the bar.
What is the shearing stress on this plane?