Question

A ${30}^{\circ },{60}^{\circ }$ triangular set square of negligible mass is suspended freely from the right angled corner and weights are hung at the two corners as shown in figure. The ratio of masses,$\frac{m_1}{m_2}$ of the weights, if the hypotenuse of the set square sets horizontally, is

• A. 3:1
• B. 1:3
• C. $1:\sqrt{3}$
• D. $\sqrt{3}:1$

Answer 1

The correct option is A 3:1

$T_{1}Sin{60}^{\circ }=m_{1}g$ $\frac{\sqrt{3}{T}_1}{2}=m,g$
$T_{2}Sin{30}^{\circ }=m_{2}g$ $\frac{T_2}{2}=m_{2}g$
$T_{1}cos{60}^{\circ }=T_{2}Cos{30}^{\circ }$
$\frac{T_1}{2}=\frac{\sqrt{3}{T}_2}{2}$
$\frac{\sqrt{3}\left(\sqrt{3}{T}_2\right)}{T_2}=\frac{m_1}{m_2}=\frac{3}{1}$