1. Tardigrade
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  3. Physics
  4. 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 θ =10° with respect to horizontal. The tension in the rope at its midpoint between the walls is

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Q. 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

Delhi UMET/DPMTDelhi UMET/DPMT 2009

Solution:

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 $ $T=\left[\frac{m g}{2 \sin 10^{\circ}}\right]$
$=\frac{0.1 \times 9.8}{2 \times 0.1736}=2.82 \,N$

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