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  4. A mass M is suspended by a rope from rigid support at A as shown in the 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 θ with the vertical, then the tension in the string AB is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-cqaci8ehqb12.png />

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Q. A mass $M$ is suspended by a rope from rigid support at $A$ as shown in the 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 $\theta $ with the vertical, then the tension in the string $AB$ is

Question

NTA AbhyasNTA Abhyas 2020Laws of Motion

Solution:

Solution
$ \frac{\mathrm{T}}{\sin 90^{\circ}}=\frac{\mathrm{F}}{\sin (\pi-\theta)}=\frac{\mathrm{Mg}}{\sin \left(\frac{\pi}{2}+\theta\right)} $
Or $\mathrm{T}=\frac{\mathrm{F}}{\sin \theta}=\frac{\mathrm{Mg}}{\cos \theta}$