question_answer

Two beams of length \[{{l}_{1}}\] and \[{{l}_{2}}\] are leaning on opposite sides of a thin vertical wall meeting at the same point on the wall and making angles \[30{}^\circ \]and \[60{}^\circ \] with it respectively. Then \[{{l}_{2}}\] is equal to

A) \[\frac{{{l}_{1}}}{2}\]

B) \[2{{l}_{1}}\]

C) \[{{l}_{1}}\sqrt{2}\]

D) \[{{l}_{1}}\sqrt{3}\]

Correct Answer: D

Solution :

 Let OW be the wall. From  \[\Delta \,AOW,\,\,\,x={{l}_{1}}\,\cos {{30}^{o}}=\frac{\sqrt{3}{{l}_{1}}}{2}\] From \[\Delta \,BOW,\] \[x={{l}_{2}}\,\cos \,{{60}^{o}}=\frac{{{l}_{2}}}{2}\] \[\therefore \]  \[\frac{{{l}_{2}}}{2}=\frac{\sqrt{3}}{2}{{l}_{1}}\] or            \[{{l}_{2}}=\sqrt{3}\,{{l}_{1}}\]