Question

suppose a cube fixed at the base and tangential force F acting on the upper face of area A , theta is shear in it , then modulus of rigidity will be ..........​

Answer 1

$\sf{Rigidity\ Modulus,}\ \boxed{\sf{G=\dfrac {F}{A\theta}}}$

Answer 2

The modulus of rigidity is $\dfrac{F}{A\theta}$

Explanation:

Given that,

Force = F

Area = A

Shear =θ

Modulus of rigidity :

Modulus of rigidity is the ratio of shear stress and shear strain.

We need to calculate the modulus of rigidity

Using formula of modulus rigidity

$G=\dfrac{\tau}{\gamma}$

Where, $\tau$ = shear stress

$\gamma$ = shear strain

Put the value into the formula

$G=\dfrac{\dfrac{F}{A}}{\dfrac{\Delta l}{l}}$

Here, $\dfrac{\Delta l}{l}=\theta$

$G=\dfrac{F}{A\theta}$

Hence, The modulus of rigidity is $\dfrac{F}{A\theta}$.

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Topic : modulus of rigidity

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