Question

An object of mass 50 kg is in a lift moving up with an acceleration of 5 ms$^{-2}$. Then the apparent weight of the object and its direction is (Acceleration due to gravity = 10 ms$^{-2}$)

• A. 750 N upwards
• B. 250 N downwards
• C. 250 N upwards
• D. 750 N downwards

Hint:

For a lift moving upwards, use \( F = m(g + a) \) to find the apparent weight. The direction is upwards as it represents the normal force.

Answer 1

The Correct Option is A

The apparent weight of an object in a lift is given by: \[ F = m(g + a) \quad (\text{if the lift is moving upwards}) \] Where:
- \( m = 50 \, \text{kg} \) (mass of the object),
- \( g = 10 \, \text{ms}^{-2} \) (acceleration due to gravity),
- \( a = 5 \, \text{ms}^{-2} \) (acceleration of the lift upwards).
Substituting the values: \[ F = 50 (10 + 5) = 50 \times 15 = 750 \, \text{N} \] Since the lift is moving upwards, the apparent weight acts in the upward direction (normal force exerted by the floor of the lift on the object).
So, the apparent weight of the object is 750 N upwards.

Answer 2

Given:
Mass, \( m = 50\, \text{kg} \)
Acceleration of lift, \( a = 5\, \text{ms}^{-2} \) (upwards)
Acceleration due to gravity, \( g = 10\, \text{ms}^{-2} \)

Apparent weight,
\[ W' = m (g + a) = 50 \times (10 + 5) = 50 \times 15 = 750\, \text{N} \]

Direction: Upwards (same as the acceleration of the lift)

Final answer:
\[ \boxed{750\, \text{N} \text{ upwards}} \]