question_answer

A wire of length L, radius r, when stretched with a force F, changes in length by I What will be the change in length in a wire of same material having length 2L, radius 2r and stretched by a force 2F?

A)  \[\frac{l}{2}\]                                   

B)  \[l\]

C)  \[2l\]                                   

D)  4L

Correct Answer: B

Solution :

                From Hookes law, the ratio of longitudinal stress to cores-ponding longitudinal strain is known as Youngs modulus of the material of wire.               \[Y=\frac{stress}{strain}=\frac{F/A}{l/L}=\frac{F/\pi {{r}^{2}}}{l/L}\]                 \[Y=\frac{F}{\pi {{r}^{2}}}\frac{L}{l}\] Given,   \[{{L}_{2}}=2L,\,{{r}_{2}}=2r\] \[\therefore \]  \[{{Y}_{2}}=\frac{2F}{\pi {{(2r)}^{2}}}.\frac{2L}{l}=Y\] Hence, change in length is same as the original.