Question

A force F is applied on the wire of radius r and length L and change in the length of wire is l. If the same force F is applied on the wire of the same material and radius 2r and length 2L, Then the change in length of the other wire is

• A. l
• B. 2l
• C. l/2
• D. 4l

Answer 1

Answer: (C)

l/2

Answer 2

$l = \frac { F L } { A Y } \Rightarrow l \propto \frac { L } { r ^ { 2 } }$ (F and Y are constant)

$\frac { l _ { 2 } } { l _ { 1 } } = \frac { L _ { 2 } } { L _ { 1 } } \times \left( \frac { r _ { 1 } } { r _ { 2 } } \right) ^ { 2 } = 2 \times \left( \frac { 1 } { 2 } \right) ^ { 2 } = \frac { 1 } { 2 }$ $\therefore l _ { 2 } = \frac { l _ { 1 } } { 2 }$

i.e. the change in the length of other wire is $\frac { l } { 2 }$