Question

Two wires of equal lengths are made of the same material. Wire A has a diameter that is twice as that of wire B. If identical weights are suspended from the ends of these wires, the increase in length is

• A. Four times for wire A as for wire B
• B. Twice for wire A as for wire B
• C. Half for wire A as for wire B
• D. One-fourth for wire A as for wire B

Answer 1

Answer: (D)

One-fourth for wire A as for wire B

Answer 2

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

$\frac { l _ { A } } { l _ { B } } = \left( \frac { r _ { B } } { r _ { A } } \right) ^ { 2 }$ $= \left( \frac { r _ { B } } { 2 r _ { B } } \right) ^ { 2 } = \frac { 1 } { 4 }$⇒ $l _ { A } = 4 l _ { B }$ or $l _ { B } = \frac { l _ { A } } { 4 }$