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A bar of uniform cross section and weighing 100 N is held horizontally using two massless and inextensible strings S1 and S2 as shown in the figure.

A bar of length L hangs from a rigid support by two vertical strings: S1 (tension T1) at its left end and S2 (tension T2) at its midpoint, L/2 from each end

The tensions in the strings are

  • A.\(T_{1}\) = 100 N and \(T_{2}\) = 0 N
  • B.\(T_{1}\) = 0 N and \(T_{2}\) = 100 N
  • C.\(T_{1}\) = 75 N and \(T_{2}\) = 25 N
  • D.\(T_{1}\) = 25 N and \(T_{2}\) = 75 N

Answer: B

The tensions are T1 = 0 N and T2 = 100 N.

The bar is uniform, so its 100 N weight acts at its midpoint, and string S2 is attached exactly there. Take moments about the midpoint: T2 has no moment arm, the weight has none either, and T1 acts L/2 away. For rotational equilibrium T1 × L/2 = 0, so T1 = 0, and vertical balance then gives T2 = 100 N.

Splitting the weight 75/25 or 25/75 would be right only if the strings were placed elsewhere, and T1 = 100 N with T2 = 0 would leave the weight with a moment about S1, so the bar would rotate.

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