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

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

TestHub · Accepted Answer

T 2 ​ cos ( 2 π ​ − θ ) = T 1 ​ cos θ ⇒ T 1 ​ cos θ = T 2 ​ sin θ T 1 ​ sin θ + T 2 ​ cos θ = 13 . ∵ OC = CA = CB ⇒ ∠ AOC = ∠ OAC and ∠ COB = ∠ OBC ∴ sin θ = sin A = 13 5 ​ and cos θ = 13 12 ​ ⇒ T 2 ​ T 1 ​ ​ = 12 5 ​ ⇒ T 1 ​ = 12 5 ​ T 2 ​ T 2 ​ ( 12 5 ​ ⋅ 13 5 ​ + 13 12 ​ ) = 13 T 2 ​ ( 12 ⋅ 13 169 ​ ) = 13 T 2 ​ = 12 kgs . ⇒ T 1 ​ = 5 kgs .

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