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Q.

A man of mass 60 kg is standing on a weighing machine kept in a box of mass 30 kg as shown in the diagram. If the man manages to keep the box stationary the reading in the weighing machine is

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a

400 N

b

300 N

c

150 N

d

600 N

answer is A.

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Detailed Solution

In the given scenario, a man weighing 60 kg stands on a weighing machine inside a 30 kg box. The box is suspended by a rope passing over a pulley, with the man holding the other end to keep the system stationary.

Calculating the Reading on the Weighing Machine:

  1. System Analysis:
    • Total Mass: Man (60 kg) + Box (30 kg) = 90 kg.
    • Gravitational Force: Total weight = 90 kg × 9.8 m/s² = 882 N.
  2. Tension in the Rope:
    • Since the system is stationary, the upward tension (T) balances the total weight:
      • 2T = 882 N (because the rope has two segments supporting the weight).
      • T = 441 N.
  3. Apparent Weight on the Weighing Machine:
    • The weighing machine measures the normal force (N) exerted by the man.
    • For the Man:
      • Downward force: Weight (W) = 60 kg × 9.8 m/s² = 588 N.
      • Upward force: Tension (T) = 441 N.
      • Apparent weight (N) = W - T = 588 N - 441 N = 147 N.
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