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

Find the tension $T_2$ for the system shown in figure.

A mass of $6 \mathrm{kg}$ is suspended by a rope of length $2 \mathrm{m}$ from a ceiling. A force of $50 \mathrm{N}$ is applied in horizontal direction at the mid-point of the rope. What is the angle between the rope and the vertical in equilibrium?

A metal sphere is hung by a string fixed to a wall. The forces acting on the sphere are shown in fig. Which of the following statements is correct ?
(a) $\overrightarrow{\mathrm{R}}+\overrightarrow{\mathrm{T}}+\overrightarrow{\mathrm{W}}=0$                 (b) T² = R² + W²
(c) T = R + W                            (d) R = W tan $\mathrm{\theta }$