Question

A steel wire can withstand a load up to $2940N$. A load of $150kg$ is suspended from a rigid support. The maximum angle through which the wire can be displaced from the mean position so that the wire does not break when the load passes through the position of equilibrium is

• A. ${30}^0$
• B. ${60}^0$
• C. ${80}^0$
• D. ${85}^0$

Answer 1

The correct option is B

${60}^0$

Step 1: Given data.

Tension of wire, $T=2940N$

Suspended mass, $m=150kg$

Step 2: Draw the free body diagram of the system.

Step 3: Finding the maximum angle through which the wire can be displaced from the mean position.

We know that,

Equilibrium at a point $B$ then,

$T\cos \theta =mg$ $\left[\because g=accelerationduetogravity\right]$

$\Rightarrow$$\cos \theta =\frac{mg}{T}$

$\Rightarrow$$\cos \theta =\frac{150\times 9.8}{2940}$ $\left[\because g=9.8m{s}^{-2}\right]$

$\Rightarrow$$\cos \theta =\frac{1}{2}$

$\Rightarrow$$\theta ={60}^0$

Hence, option B is correct.