Two wires A and B of same length and of the same material have the respective radii $r_{1}$ and $r_{2}$ . Their one end is fixed with a rigid support, and at the other end equal twisting couple is applied. Then the ratio of the angle of twist at the end of A and the angle of twist at the end of B will be

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

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

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

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

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Solution

The correct option is C $\frac{r_{2}^{4}}{r_{1}^{4}}$
$r_{1} = r_{2} \Rightarrow \frac{π η r_{1}^{4} θ_{1}}{2 l_{1}} = \frac{π η r_{2}^{4} θ_{2}}{2 l_{2}} \Rightarrow \frac{θ_{1}}{θ_{2}} = {(\frac{r_{2}}{r_{1}})}^{4}$
When strain is unity then Young's modulus is equal to stress.

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Two wires A and B of same length and of the same material have the respective radii r1 and r2. Their one end is fixed with a rigid support, and at the other end equal twisting couple is applied. Then the ratio of the angle of twist at the end of A and the angle of twist at the end of B will be

The correct option is C r42r41r1=r2⇒πηr41θ12l1=πηr42θ22l2⇒θ1θ2=(r2r1)4 When strain is unity then Young's modulus is equal to stress.

The correct option is C $\frac{r_{2}^{4}}{r_{1}^{4}}$
$r_{1} = r_{2} \Rightarrow \frac{π η r_{1}^{4} θ_{1}}{2 l_{1}} = \frac{π η r_{2}^{4} θ_{2}}{2 l_{2}} \Rightarrow \frac{θ_{1}}{θ_{2}} = {(\frac{r_{2}}{r_{1}})}^{4}$
When strain is unity then Young's modulus is equal to stress.