First slide

Connected bodies

Question

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

Moderate

A

Fsinq
B

F/sinq
C

Fcosq
D

F/cosq

Solution

Different forces are shown in fig.
In fig., the point I is in equilibrium under the action of X, F and Mg. Here
$T = AB = CB / \sin θ = F / \sin θ or F = Tsin θ$
Also, $T = AB = AC / \cos θ = Mg / \cos θ$
$or Mg = Tcos θ$
$∴ T^{2} = F^{2} + (Mg)^{2} or T = {[F^{2} + (Mg)^{2}]}^{1 / 2}$ .

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