question_answer

A triangular set square of angles \[30{}^\circ ,\text{ }60{}^\circ ,\text{ }90{}^\circ \] and of negligible mass is suspended freely from the right angled comer and weights are hung at the two comers. If the hypotenuse of the set square sets horizontally, then the ratio of the weights \[{{W}_{1}}/{{W}_{2}}\] is

A) \[1:1\]              

B) \[1:3\]

C) \[\sqrt{3}:1\]    

D) \[1:\sqrt{3}\]

Correct Answer: B

Solution :

[b]  \[AB=l,\text{ }AD=A\text{ }cos30{}^\circ =l~cos30{}^\circ \text{ }cos30{}^\circ \] \[BD=BC\text{ }cos60{}^\circ =l~cos60{}^\circ \text{ }cos60{}^\circ \] \[{{W}_{1}}(AD)={{W}_{2}}(BD)\Rightarrow \frac{{{W}_{1}}}{{{W}_{2}}}=\frac{1}{3}\]