When a lift moves upward with an acceleration, how does the apparent weight of a person or body inside the lift compare with its true weight?

Introduction / Context:
Questions involving a person standing in an accelerating lift are standard applications of Newton laws of motion. They help students understand the idea of apparent weight and how it changes when the lift accelerates upward or downward. This question asks what happens to the apparent weight of a body when the lift is going up with an acceleration, a case that occurs in many real life situations such as high speed elevators.

Given Data / Assumptions:

• A body of mass m is standing on a weighing machine inside a lift.
• The lift is moving upward with acceleration a, in addition to the acceleration due to gravity g.
• The apparent weight is the normal reaction shown by the weighing machine.
• We neglect friction and assume vertical motion only.

Concept / Approach:
The true weight of a body is given by W = m * g, where g is acceleration due to gravity. In an accelerating frame like a lift, the normal reaction between the body and the floor changes. When the lift accelerates upward, the floor must push harder on the body to produce the net upward acceleration. The weighing machine measures this normal reaction. Therefore, in an upward accelerating lift, the apparent weight R becomes m * (g + a), which is greater than m * g.

Step-by-Step Solution:
Step 1: Draw a free body diagram for the body in the lift, showing weight m * g downward and normal reaction R upward. Step 2: Since the lift accelerates upward with acceleration a, the body also accelerates upward with acceleration a. Step 3: Apply Newton second law in the upward direction: R minus m * g equals m * a. Step 4: Rearrange to get R = m * g + m * a = m * (g + a). Step 5: Because a is positive when the lift accelerates upward, g + a is greater than g, so R is greater than the true weight m * g.

Verification / Alternative check:
You can check limiting cases. If the acceleration a is zero, the lift moves at constant velocity and R becomes m * g, equal to the true weight. If the lift suddenly accelerates upward strongly, you feel heavier and the weighing machine would show a larger reading, which matches the formula R = m * (g + a). These physical sensations confirm that apparent weight increases when the lift accelerates upward.

Why Other Options Are Wrong:
It may be more or less than the true weight is too vague and does not describe the specific case of upward acceleration.
It is less than the true weight is the situation for downward acceleration, not upward acceleration.
It is equal to the true weight is correct only when the lift has no acceleration.
It becomes zero for any acceleration is incorrect, as zero apparent weight occurs only in free fall when acceleration equals g downward.

Common Pitfalls:
A common mistake is to think that velocity and acceleration have the same effect. Students sometimes confuse a lift moving upward at constant speed with a lift accelerating upward. Another pitfall is forgetting the direction when applying Newton second law, which can lead to sign errors. Always set up the free body diagram, choose a consistent direction as positive and write the equation of motion carefully.

Final Answer:
When the lift goes up with acceleration, the apparent weight of the body is more than the true weight.