Question

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} $

Answer 1

Answer: (D)

Different forces acting on the boy are shown in figure.

In equilibrium
$2 T \cos \theta =m g$
$T =\frac{m g}{2 \cos \theta}$
Tension will be maximum,
when value of $2 \cos \theta$ is $1$
If $\theta=60^{\circ}$
Then, $2 \cos \theta=2 \cos 60^{\circ} $
$=2 \times \frac{1}{2}=1$
So, angle between the arms
$=2 \times 60=120^{\circ}$