question_answer

A boy is hanging from a horizontal branch of a tree. The tension in the arms will be maximum when the angle between the arms is

A)  \[0{}^\circ \]                                     

B)  \[60{}^\circ \]

C)   \[90{}^\circ \]                                 

D) \[120{}^\circ \]

Correct Answer: D

Solution :

                 Different forces acting on the boy are shown in figure. In equilibrium                 \[2T\cos \theta =mg\]                 \[T=\frac{mg}{2\cos \theta }\] Tension will be maximum, when value of\[2\cos \theta \]is 1. If             \[\theta =60{}^\circ \]    Then,   \[2cos\theta =2cos{{60}^{o}}=2\times \frac{1}{2}=1\] So, angle between the arms\[=2\times 60=120{}^\circ \]