Question

Two wires of the same material have lengths in the ratio 1 : 2 and their radii are in the ratio $1 : \sqrt { 2 }$. If they are stretched by applying equal forces, the increase in their lengths will be in the ratio

• A. $2 : \sqrt { 2 }$
• B. $\sqrt { 2 } : 2$
• C. 1 : 1
• D. 1 : 2

Answer 1

Answer: (C)

1 : 1

Answer 2

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

$\frac { l _ { 1 } } { l _ { 2 } } = \frac { L _ { 1 } } { L _ { 2 } } \left( \frac { r _ { 2 } } { r _ { 1 } } \right) ^ { 2 } = \frac { 1 } { 2 } ( \sqrt { 2 } ) ^ { 2 }$∴$\frac { l _ { 1 } } { l _ { 2 } } = 1 : 1$