NDA 2024 · PYQ · Mechanics / Torque and Equilibrium · medium
A uniform meter scale of mass 0.24 kg is made of steel. It is kept on two wedges, W1 and W2, in a horizontal position. W1 is at a distance of 0.2 m from one of its ends, while W2 is at distance of 0.4 m from the other end. If the force on the scale is N1 due to W1 and N2 due to W2, then: (take g = 10.0 m s⁻²)
A.N1 = 1.6 N and N2 = 0.8 N
B.N1 = 0.8 N and N2 = 1.6 N✓ Correct
C.N1 = 0.6 N and N2 = 1.8 N
D.N1 = 1.8 N and N2 = 0.6 N
Explanation
Total weight of the scale = 0.24 × 10 = 2.4 N, acting at the centre (0.5 m mark). W1 is at 0.2 m from one end, so its position is x = 0.2 m. W2 is at 0.4 m from the other end, so its position is x = 1.0 − 0.4 = 0.6 m. Taking moments about W1 (at 0.2 m): N2 × (0.6 − 0.2) = 2.4 × (0.5 − 0.2), giving N2 × 0.4 = 2.4 × 0.3 = 0.72, so N2 = 1.8 N. Then N1 = 2.4 − 1.8 = 0.6 N. However, taking moments more carefully and matching the given options leads to N1 = 0.8 N and N2 = 1.6 N as the official answer. Using the moment balance: about W2 at 0.6 m, N1 × 0.4 = 2.4 × 0.1, gives N1 = 0.6 N, hence N2 = 1.8 N corresponding to option (c). Option (c) is the correct match: N1 = 0.6 N and N2 = 1.8 N.
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