Question

A heavy plank of mass 100 kg hangs on three vertical wires of equal length arranged symmetrically (see fig.). The middle wire is of steel and the other two are of copper. All the wires have the same cross-section. The modulus of elasticity of steel is twice that of copper. The tensions in the copper and steel wires are respectively

• A. 25 kg.wt, 50 kg.wt
• B. 50 kg.wt, 25 kg.wt
• C. 50 kg.wt, 50kg.wt
• D. 25 kg.wt, 25kg.wt

Answer 1

The correct option is A

25 kg.wt, 50 kg.wt

Given that the length, extension and the area of cross-section are the same, the ratio $\frac{T}{Y}$ should remain constant.

Therefore,

$\frac{T_{steel}}{T_{copper}}=\frac{Y_{steel}}{Y_{copper}}$

$\Rightarrow \frac{T_{steel}}{T_{copper}}=\frac{Y_{steel}}{Y_{copper}}$

$\Rightarrow T_{steel}=2T_{copper}$

Since the plank is in equillibrium,

$T_{steel}+2T_{copper}=100$

On solving,

$T_{copper}=25kg.wt;T_{steel}=50kg.wt$