Question

A block of mass \( M \) is placed on the floor of a lift at the center. The acceleration required for the lift to descend so that the block exerts a force of \( \frac{Mg}{4} \) on the lift floor is:

• A. \( g \)
• B. \( \frac{g}{4} \)
• C. \( \frac{g}{3} \)
• D. \( \frac{2g}{3} \)
• E. \( \frac{3g}{4} \)

Hint:

The effective weight of an object in an accelerating lift depends on both gravity and the lift’s motion.

Answer 1

Answer: (E)

The normal force exerted by the block on the lift floor is: \[ N = Mg - Ma \] Given \( N = \frac{Mg}{4} \), solving for \( a \): \[ Mg - Ma = \frac{Mg}{4} \] \[ Mg - \frac{Mg}{4} = Ma \] \[ \frac{3Mg}{4} = Ma \] \[ a = \frac{3g}{4} \]