Question

Increase in length of a wire is 1 mm when suspended by a weight. If the same weight is suspended on a wire of double its length and double its radius, the increase in length will be

• A. 2 mm
• B. 0.5 mm
• C. 4 mm
• D. 0.25 mm

Answer 1

Answer: (B)

0.5 mm

Answer 2

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

∴$\frac { l _ { 2 } } { l _ { 1 } } = \frac { L _ { 2 } } { L _ { 1 } } \left( \frac { r _ { 1 } } { r _ { 2 } } \right) ^ { 2 } = 2 \times \left( \frac { 1 } { 2 } \right) ^ { 2 } = \frac { 1 } { 2 }$ ⇒$l _ { 2 } = \frac { l _ { 1 } } { 2 } = \frac { l } { 2 } = 0.5 \mathrm {~mm}$