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Q.

A mass M is suspended by a rope from a rigid support at A as shown in fig. Another rope istied at the end 8, and it is pulled horizontally with a force F. If the rope AB makes an angle q with the vedical, then the tension in the string AB is

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a

Fsinq

b

F/sinq

c

Fcosq

d

F/cosq

answer is B.

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Detailed Solution

Different forces are shown in fig. In fig., the point I is in equilibrium under the action of X, F and Mg. HereT=AB=CB/sin⁡θ=F/sin⁡θ or F=Tsin⁡θAlso, T=AB=AC/cos⁡θ=Mg/cos⁡θ or Mg=Tcos⁡θ∴ T2=F2+(Mg)2 or T=F2+(Mg)21/2.
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