Question

When a uniform wire of radius r is stretched by a 2kg weight, the increase in its length is 2.00 mm. If the radius of the wire is r/2 and other conditions remain the same, the increase in its length is

• A. 2.00 mm
• B. 4.00 mm
• C. 6.00mm
• D. 8.00 mm

Answer 1

Answer: (D)

8.00 mm

Answer 2

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

$\frac { l _ { 2 } } { l _ { 1 } } = \left( \frac { r _ { 1 } } { r _ { 2 } } \right) ^ { 2 } = ( 2 ) ^ { 2 } \Rightarrow l _ { 2 } = 4 l _ { 1 } = 4 \times 2 = 8 \mathrm {~mm}$