Question:
A man of mass \(60 \text{ kg}\) is standing in a lift moving up with a retardation of \(2.8 \text{ ms}^{-2}\). The apparent weight of the man is
A man of mass \(60 \text{ kg}\) is standing in a lift moving up with a retardation of \(2.8 \text{ ms}^{-2}\). The apparent weight of the man is
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"Moving up with retardation" is physically equivalent to "moving down with acceleration". In both cases, the apparent weight becomes less than the true weight, so \(W = m(g - a)\).
Updated On: May 9, 2026
- \(756 \text{ N}\)
- \(168 \text{ N}\)
- \(588 \text{ N}\)
- \(420 \text{ N}\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Question:
We need to calculate the apparent weight of a person in a lift. The lift is moving upwards but experiencing retardation, which means the acceleration vector is directed downwards.
Step 2: Key Formula or Approach:
The apparent weight (\(W_{app}\)) in a vertically moving frame is given by the normal reaction force: \[ W_{app} = m(g + a) \] where \(a\) is the acceleration of the lift taking upwards as positive. If the lift is retarding while moving upwards, \(a\) is negative.
Step 3: Detailed Explanation:
Given values:
Mass of the man, \(m = 60 \text{ kg}\)
Acceleration due to gravity, \(g = 9.8 \text{ m/s}^2\) (Standard value)
Upward acceleration, \(a = -2.8 \text{ m/s}^2\) (since it is a retardation while moving up).
Substitute these values into the apparent weight formula: \[ W_{app} = 60 \times (9.8 - 2.8) \] \[ W_{app} = 60 \times 7.0 \] \[ W_{app} = 420 \text{ N} \] Step 4: Final Answer:
The apparent weight of the man is \(420 \text{ N}\).
We need to calculate the apparent weight of a person in a lift. The lift is moving upwards but experiencing retardation, which means the acceleration vector is directed downwards.
Step 2: Key Formula or Approach:
The apparent weight (\(W_{app}\)) in a vertically moving frame is given by the normal reaction force: \[ W_{app} = m(g + a) \] where \(a\) is the acceleration of the lift taking upwards as positive. If the lift is retarding while moving upwards, \(a\) is negative.
Step 3: Detailed Explanation:
Given values:
Mass of the man, \(m = 60 \text{ kg}\)
Acceleration due to gravity, \(g = 9.8 \text{ m/s}^2\) (Standard value)
Upward acceleration, \(a = -2.8 \text{ m/s}^2\) (since it is a retardation while moving up).
Substitute these values into the apparent weight formula: \[ W_{app} = 60 \times (9.8 - 2.8) \] \[ W_{app} = 60 \times 7.0 \] \[ W_{app} = 420 \text{ N} \] Step 4: Final Answer:
The apparent weight of the man is \(420 \text{ N}\).
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