A girl stands on a scale in a lift. If the reading on the scale is less than her weight, then the lift is moving

Analyze the question: The scale reads the normal force (R) the floor exerts on the girl, which is her apparent weight. We need to find which motion makes R less than her true weight (mg).

Concept: Apply Newton's second law to the girl, taking upward as positive:

R − mg = ma

• Uniform speed (up or down): a = 0, so R = mg. The reading equals her weight.
• Accelerating upward: a > 0, so R = m(g + a), which is greater than mg.
• Accelerating downward: a is negative, so R = m(g − a), which is less than mg.

Check each option:

• A. Upward at uniform speed: R = mg. Not less. ✗
• B. Upward with uniform acceleration: R = m(g + a), which is greater than mg. ✗
• C. Downward at uniform speed: R = mg. ✗
• D. Downward with uniform acceleration: R = m(g − a), which is less than mg. ✓

Note: Strictly, a downward acceleration is what matters. A lift moving upward but slowing down also has a downward acceleration and would give a smaller reading. Among the options given, only D fits.

Tip: Think of how your stomach feels when a lift starts going down: you feel lighter. Accelerating up makes you feel heavier and accelerating down makes you feel lighter. Constant speed means no change in the reading.