Question

Two wires ‘A’ and ‘B’ of the same material have radii in the ratio 2 : 1 and lengths in the ratio 4 : 1. The ratio of the normal forces required to produce the same change in the lengths of these two wires is

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

Answer 1

Answer: (A)

1 : 1

Answer 2

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

∴$\frac { F _ { 1 } } { F _ { 2 } } = \left( \frac { r _ { 1 } } { r _ { 2 } } \right) ^ { 2 } \left( \frac { L _ { 2 } } { L _ { 1 } } \right) = \left( \frac { 2 } { 1 } \right) ^ { 2 } \left( \frac { 1 } { 4 } \right) = 1$⇒ $\frac { F _ { 1 } } { F _ { 2 } } = 1 : 1$