A uniform rope is tied between two nails A and B, first one on vertical wall and the second one on the ground. In equilibrium rope assumes a curved shape as A and B are not on the same vertical line. Tangents to the rope’s shape make angles $α$ and $β$ respectively with vertical. Which of the following can be concluded?

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$α$ can be greater than $β$

vertical component of tension in the rope increases with height

Horizontal component of tension in the rope is uniform

$α \neq 0^{o}$

answer is A, B, D.

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Detailed Solution

Write eqns for equilibrium of rope in horizontal and vertical directions.

$\Rightarrow$ Horizontal component remains same whereas vertical component increases as we move up due to weight.

If ‘ $θ$ ’ is angle with vertical $\Rightarrow T \sin θ$ is constant so a ‘ $θ$ ’ changes from $β$ to $α$ ,

$T \sin θ$ is const and $T \cos θ$ increases $\Rightarrow$ T increases and $α < β$

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