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Question: A mass M is suspended by a rope from a rigid support at A as shown in figure. Another rope is tied a...

A mass M is suspended by a rope from a rigid support at A as shown in figure. Another rope is tied at the end B and it is pulled horizontally with a force F. If the rope AB makes an angle q with the vertical, then the tension in the string AB is –

A

F sin q

B

F/sin q

C

F cosq

D

F/cosq

Answer

F/sin q

Explanation

Solution

Tsin⁡90∘=Fsin⁡(π−θ)=Mgsin⁡(π2+θ)\frac { T } { \sin 90 ^ { \circ } } = \frac { F } { \sin ( \pi - \theta ) } = \frac { M g } { \sin \left( \frac { \pi } { 2 } + \theta \right) }

or T = Fsin⁡θ=Mgcos⁡θ\frac { F } { \sin \theta } = \frac { M g } { \cos \theta }