Two wires A and B are of same materials. Their length are in the ratio 3: 4 and diameters are in the ratio 5: 1 when stretched by force FA and FB respectively they get equal in increase in their lengths. The ratio of FB/FA is.

Question

Two wires A and B are of same materials. Their length are in the ratio 3: 4 and diameters are in the ratio 5: 1 when stretched by force FA and FB respectively they get equal in increase in their lengths. The ratio of FB/FA is. (A) 0.01 (B) 0.03 (C) 0.04 (D) 0.05

Tardigrade Admin · Accepted Answer

F =(Y A Δ L/L) F propto (r2/L) ∴ (FB/FA) =(rB2/(rA)2) × (LA/LB)=((1/5))2 × (3/4) =(3/4) × (1/25)=0.03

Q. Two wires A and B are of same materials. Their length are in the ratio 3 : 4 and diameters are in the ratio $5 : 1$ when stretched by force $F_{A}$ and $F_{B}$ respectively they get equal in increase in their lengths. The ratio of $F_{B} / F_{A}$ is.

0.01

0.03

0.04

0.05

$F = \frac{Y A Δ L}{L}$
$F \propto \frac{r ^{2}}{L}$
$∴ \frac{F _{B}}{F _{A}} = \frac{r _{B}^{2}}{( r _{A} ) ^{2}} \times \frac{L _{A}}{L _{B}} = (\frac{1}{5})^{2} \times \frac{3}{4}$
$= \frac{3}{4} \times \frac{1}{25} = 0.03$

Q. Two wires A and B are of same materials. Their length are in the ratio 3 : 4 and diameters are in the ratio 5:1 when stretched by force FA​ and FB​ respectively they get equal in increase in their lengths. The ratio of FB​/FA​ is.