Two wires A and B of the same length and of t | vedclass

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Question

(C) The twisting couple $C$ required to produce an angle of twist $	heta$ in a wire of length $l$,radius $r$,and modulus of rigidity $\eta$ is given

Vedclass · Accepted Answer

$r_2^4 / r_1^4$

Vedclass · Answer

(C) The twisting couple $C$ required to produce an angle of twist $	heta$ in a wire of length $l$,radius $r$,and modulus of rigidity $\eta$ is given by the formula:$C = \frac{\pi \eta r^4 	heta}{2l}$From this expression,we can see that for a constant twisting couple $C$,length $l$,and material property $\eta$:$	heta = \frac{2lC}{\pi \eta r^4}$This implies that $	heta \propto \frac{1}{r^4}$.Therefore,for wires $A$ and $B$ with radii $r_1$ and $r_2$ respectively,the ratio of the angles of twist $	heta_1$ and $	heta_2$ is:$\frac{	heta_1}{	heta_2} = \frac{r_2^4}{r_1^4}$Thus,the correct option is $C$.

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