Question

A steel and a brass wire, each of length 50 cm and cross-sectional area $0.005c{m}^2$ hang from a ceiling and are 15 cm apart. Lower ends of the wires are attached to a light horizontal bar. A suitable downward load is applied to the bar so that each of the wires extends in length by 0.1 cm. At what distance from the steel wire the load must be appied?

[Young's modulus of steel is $2\times {10}^{12}dynes/c{m}^2$] and that of brass is $1\times {10}^{12}dynes/c{m}^2$

• A. 7.5 cm
• B. 5 cm
• C. 10 cm
• D. 3 cm

Answer 1

Answer: (B)

. 5 cm.

We know that,
$F=\frac{AYl}{L}$;
As $A,L$ and $l$ are the same for both wires, therefore,

$F\propto Y$

Let the distance of the application of the load from the steel wire be $x$.

Now taking moments about the point of application of the load we get,

$F_s\left(x\right)=F_b(15-x)$

$\Rightarrow Y_s\left(x\right)=Y_b(15-x)$

Since $Y_s=2Y_b$ we get,

$\Rightarrow 2x=(15-x)$

$\Rightarrow x=5cm$.

Thus the load must be applied at a distance of 5 cm from the steel wire.