The actual weight of a person is mg. When the lift is moving uniformly in upward direction, the apparent weight of the person in lift will be :

Question

Accepted Answer

When a lift is moving uniformly in an upward direction, the apparent weight of a person inside the lift is equal to their actual weight. This is because when the lift moves at a constant velocity, there is no net acceleration acting on the person other than gravity. Therefore, the forces acting on the person are balanced, and the apparent weight is simply the gravitational force acting on them, which is mg.

Let's analyze why Option 2 is correct and why the other options are incorrect:

1. **Option 2 (mg):** This is the correct answer. When the lift moves uniformly (at constant speed) in an upward direction, there is no additional acceleration affecting the person other than gravity. The apparent weight is the same as the actual weight, which is mg. This is because the net force on the person is zero, as the upward force from the lift counteracts the gravitational force.

2. **Option 1 (zero):** This option is incorrect because the apparent weight of the person cannot be zero unless the lift is in free fall. In free fall, both the lift and the person would be accelerating downward at the same rate due to gravity, making the apparent weight zero. However, in this scenario, the lift is moving uniformly, not accelerating, so the apparent weight remains mg.

3. **Option 3 (m(g + a)):** This option is incorrect because it represents the apparent weight when the lift is accelerating upwards with an acceleration 'a'. In such a case, the apparent weight would indeed be m(g + a). However, since the lift is moving uniformly (constant velocity), there is no additional acceleration, and the apparent weight is simply mg.

4. **Option 4 (m(g - a)):** This option is incorrect because it represents the apparent weight when the lift is accelerating downwards with an acceleration 'a'. In that scenario, the apparent weight would be m(g - a). Since the lift is moving uniformly upwards, there is no downward acceleration, and the apparent weight remains mg.

In conclusion, when the lift moves uniformly in an upward direction, the apparent weight of the person is equal to their actual weight, mg, making Option 2 the correct choice.