Question

The extension of a wire by the application of load is 3 mm. The extension in a wire of the same material and length but half the radius by the same load is

• A. 12 mm
• B. 0.75 mm
• C. 15 mm
• D. 6 mm

Answer 1

Answer: (A)

12 mm

Answer 2

$l = \frac { F L } { A Y } \Rightarrow l \propto \frac { 1 } { r ^ { 2 } }$ (F,L and Y are constant)

$\frac { l _ { 2 } } { l _ { 1 } } = \left( \frac { r _ { 1 } } { r _ { 2 } } \right) ^ { 2 } = ( 2 ) ^ { 2 } \Rightarrow l _ { 2 } = 4 l _ { 1 } = 4 \times 3 = 12 \mathrm {~mm}$