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NDA 1 2024 GAT, question 83

Topic: Physics

Q83

A uniform meter scale of mass 0.24 kg0.24\text{ kg} is made of steel. It is kept on two wedges, W1W_{1} and W2W_{2}, in a horizontal position. W1W_{1} is at a distance of 0.2 m0.2\text{ m} from one of its ends, while W2W_{2} is at distance of 0.4 m0.4\text{ m} from the other end. If the force on the scale is N1N_{1} due to W1W_{1} and N2N_{2} due to W2W_{2}, then : (take g=10.0 m s−2g=10.0\text{ m s}^{-2})

  1. (a) N1=1.6 NN_{1}=1.6\text{ N} and N2=0.8 NN_{2}=0.8\text{ N}
  2. (b) N1=0.8 NN_{1}=0.8\text{ N} and N2=1.6 NN_{2}=1.6\text{ N}
  3. (c) N1=0.6 NN_{1}=0.6\text{ N} and N2=1.8 NN_{2}=1.8\text{ N}Correct answer
  4. (d) N1=1.8 NN_{1}=1.8\text{ N} and N2=0.6 NN_{2}=0.6\text{ N}

Solution.

Answer: (c) N1=0.6 NN_{1}=0.6\text{ N} and N2=1.8 NN_{2}=1.8\text{ N}

  1. Take the left end as 0: W₁ is at 0.2 m, W₂ at 0.6 m, and the centre of mass at 0.5 m.
  2. Weight is 0.24 × 10 = 2.4 N.
  3. Moments about W₁ give 0.4N₂ = 0.3 × 2.4, hence N₂ = 1.8 N.
  4. Force balance gives N₁ = 0.6 N.