A body of mass m is suspended by two strings making angles θ₁ and θ₂ with the horizontal ceiling. The corresponding tensions are T₁ and T₂, and T₁ = √3 T₂. Which option is correct?
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Question

A body of mass m is suspended by two strings making angles θ₁ and θ₂ with the horizontal ceiling. The corresponding tensions are T₁ and T₂, and T₁ = √3 T₂. Which option is correct?

G1 Physics · Accepted Answer

For equilibrium, horizontal components of tension must balance: T₁cosθ₁ = T₂cosθ₂. Given T₁ = √3 T₂, we need √3 cosθ₁ = cosθ₂. The pair θ₁ = 60°, θ₂ = 30° satisfies this because √3 cos60° = √3/2 = cos30°. Now use vertical equilibrium: T₁sin60° + T₂sin30° = mg. Substitute T₁ = √3T₂: (√3T₂)(√3/2) + T₂(1/2) = mg ⇒ (3/2 + 1/2)T₂ = mg ⇒ 2T₂ = mg ⇒ T₂ = mg/2. Correct option: A.