Question

Let $ABC$ be an equilateral triangle formed by weightless inextensible strings, the side $AB$ is horizontal. $A$ and $B$ are tied to fixed points $D$and $E$ by equal weightless inextensible strings $AD,BE;$ a weight of W gm is attached at $C$. The angle $DAB,ABE$ are each $150°$. Then which of the following statements is true?

• A. The tensions in the strings $AB$, $BC$ and $CA$ are equal
• B. The tensions in the strings $BE$, $AD$ are inversely proportional
• C. The tension in $BE$ is less than the tension in $AB$
• D. The tension in $AD$ is twice the tension in $BC$

Answer 1

The correct option is A

The tensions in the strings $AB$, $BC$ and $CA$ are equal

Explanation for the correct option:

Finding which of the following statements is true.

Given: $ABC$ is an equilateral triangle. The angle $DAB,ABE$ are each $150°$

From the figure,

$$\begin{gathered} T_{AC}\sin 30°=T_{BC}\sin 30° \\ {T}_{AC}=T_{BC} \end{gathered}$$ since,

$$\begin{gathered} 2T_{AC}\cos 30°=W \\ \sin 60°T_{DA}=\sin 150°T_{AB}=\sin 150°T_{AC} \end{gathered}$$

$\Rightarrow T_{AB}=T_{AC}=\frac{W}{\sqrt{3}}$

Hence, option A is correct.