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 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
Updated On: Jan 18, 2023
- 2.78 N
- 2.56 N
- 2.82 N
- 2.71 N
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The Correct Option is C
Solution and Explanation
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} $
$\therefore$ $T=\left[\frac{m g}{2 \sin 10^{\circ}}\right]$
$=\frac{0.1 \times 9.8}{2 \times 0.1736}=2.82 \,N$
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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Concepts Used:
Tension
A force working along the length of a medium, especially if this force is carried by a flexible medium like cable or rope is called tension. The flexible cords which bear muscle forces to other parts of the body are called tendons.
Net force = 𝐹𝑛𝑒𝑡 = 𝑇−𝑊=0,
where,
T and W are the magnitudes of the tension and weight and their signs indicate a direction, be up-front positive here.
Read More: Tension Formula