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Q44 (NDA-II/2011) Science & Technology › Basic Science (Physics, Chemistry, Biology) › Basic mechanics concepts Answer Verified

If the ratio of the weight of a man in a stationary lift and when it is moving downwards with uniform acceleration ‘a’ is 3 : 2, then the value of‘a’ is

Result
Your answer: —  ·  Correct: B
Explanation

The weight of a man in a stationary lift is his true weight, given by W = mg. When the lift moves downwards with uniform acceleration 'a', the apparent weight (N) decreases because the normal force must only counteract the net force remaining after acceleration. The formula for apparent weight during downward acceleration is N = m(g - a). According to the problem, the ratio of stationary weight to downward accelerating weight is 3:2. Therefore, mg / m(g - a) = 3 / 2. Simplifying this equation: 2mg = 3m(g - a), which leads to 2g = 3g - 3a. Rearranging the terms gives 3a = g, resulting in a = g/3. This confirms that the acceleration required to reduce the apparent weight to two-thirds of the true weight is one-third of the acceleration due to gravity.

Sources

  1. [1] Science ,Class VIII . NCERT(Revised ed 2025) > Chapter 5: Exploring Forces > 5.5 Weight and Its Measurement > p. 72
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