Question

A rope of mass $0.1\, kg$ is connected at the same height of two opposite walls. It is allowed to hang under its own weight. At [he contact point between the rope and the wall, the rope makes an angle $\theta =10^{\circ}$ with respect to horizontal. The tension in the rope at its midpoint between the walls is

• A. 2.78 N
• B. 2.56 N
• C. 2.82 N
• D. 2.71 N

Answer 1

Answer: (C)

2.82 N

Answer 2

Let the tension in each section $A B$ and $A C$ be $T$.
Now, from the condition of equilibrium it is clear that the horizontal components are equal in magnitude and opposite to each other so they cancel out each other.
Hence, $m g=2 T \sin 10^{\circ}$
$\therefore$ $T=\left[\frac{m g}{2 \sin 10^{\circ}}\right]$
$=\frac{0.1 \times 9.8}{2 \times 0.1736}=2.82 \,N$