Question

Let $ABC$ be an equilateral triangle formed by weigthless 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 ${150}^o$. 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

$T_{AC}\sin {30}^o=T_{BC}\sin {30}^o$
$T_{AC}=T_{BC}\therefore 2T_{AC}\cos {30}^o=W$
$\frac{T_{DA}=}{\sin {60}^o}=\frac{T_{AB}=}{\sin {150}^o}=\frac{T_{AC}}{\sin {150}^o}$
$\therefore T_{AB}=T_{AC}=\frac{W}{\sqrt{3}}$