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Shear Modulus

Two rods A an...

Question

Two rods A and B of the same material and length have their radii $r_{1}$ and $r_{2}$ respectively. When they are rigidly fixed at one end and twisted by the same couple applied at the other end, the ratio of the angle of twist at the end of A and the angle of twist at the end of B is

A

\frac{r_{2}^{4}}{r_{1}^{4}}

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B

\frac{r_{1}^{4}}{r_{2}^{4}}

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C

\frac{r_{2}^{2}}{r_{1}^{2}}

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D

\frac{r_{1}^{2}}{r_{2}^{2}}

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Solution

The correct option is A $\frac{r_{2}^{4}}{r_{1}^{4}}$
$τ = \frac{π n r^{4}}{21} θ$
In the given problem, $r^{4} θ =$ constant
Therefore $\frac{θ_{A}}{θ_{B}} = \frac{r_{2}^{4}}{r_{1}^{4}}$

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