Question

The ratio of the lengths of two wires A and B of same material is 1 : 2 and the ratio of their diameter is 2 : 1. They are stretched by the same force, then the ratio of increase in length will be

• A. 2 : 1
• B. 1 : 4
• C. 1 : 8
• D. 8 : 1

Answer 1

Answer: (C)

1 : 8

Answer 2

$l = \frac { F L } { A Y } \Rightarrow l \propto \frac { L } { d ^ { 2 } }$⇒$\frac { l _ { 1 } } { l _ { 2 } } = \frac { L _ { 1 } } { L _ { 2 } } \times \left( \frac { d _ { 2 } } { d _ { 1 } } \right) ^ { 2 }$ $= \frac { 1 } { 2 } \times \left( \frac { 1 } { 2 } \right) ^ { 2 } = \frac { 1 } { 8 }$