Question

Two wires A and B are of same material. Their lengths are in the ratio 1:2 and diameters are in ratio 2:1. When stretched by force F^A and F^B respectively, they get equal increase in lengths. The ratio of F^A / F^B should be......

Answer 1

Answer:

Ratio of F^A to F^B = 8 : 1

Explanation:

$Y = \frac{F/A}{l/L}$    l is change in length of wire

                 L is length of wire

l, Y are constants (Y is young's modulus, material constant)

$F = \frac{YAl}{L}$

F ∝ 1 /L

F ∝ A

$\frac{F_{A} }{F_{B} } = \frac{A_{A} }{A_{B} } \frac{L_{B} }{L_{A} }$

     $= \frac{4}{1} \frac{2}{1}$ = 8 : 1