Math miscellaneousHard

Question

A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are

Options

A.12 kg and 13 kg
B.5 kg and 5 kg
C.5 kg and 12 kg
D.5 kg and 13 kg

Solution

         
T2 cos = T1 cos θ ⇒ T1 cos θ = T2 sin θ
T1 sin θ + T2 cos θ = 13.
∵     OC = CA = CB
⇒     ∠AOC = ∠OAC and ∠COB = ∠OBC
∴     sin θ = sin A = and cos θ =
⇒     ⇒ T1 = T2
T2 = 13
T2 = 13
T2 = 12 kgs. ⇒ T1 = 5 kgs.

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