Question

A steel and a brass wire, each of length $50cm$ and cross-sectional area $0.005c{m}^2$ hang from a ceiling and are $15cm$ 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 $0.1cm$. At what distance from the steel wire the load must be applied?
[Young's modulus of steel is $2\times 10^{12}$ dynes/cm ${}^2$ 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)

At equilibrium, Taking torque about point O
$T_{1}x=T_2(15-x)$
$\Rightarrow Y_{1}x=Y_2(15-x)$
$\left[Y=\frac{T}{A}\times \frac{L}{l};T\propto Y\right]$
$1\times 10^{12}x=2\times 10^{12}(15-x);3x=15,$
So, $x=5cm$