Question

A wooden cube is floating in a bucket of water with \(\frac{3}{4}\) of its volume immersed. If this bucket with the wooden block is now placed in a lift moving down with an acceleration of \(\frac{g}{2}\), the fraction of volume of the wooden cube immersed in water is:

• A. \(\frac{3}{4}\)
• B. \(\frac{3}{8}\)
• C. \(\frac{3}{2}\)
• D. \(\frac{1}{2}\)

Hint:

When the lift is accelerating down, the apparent weight of the object decreases, but the fraction of the object immersed in a fluid may remain unchanged in some conditions.

Answer 1

The Correct Option is A

When a wooden cube is floating in water, the fraction of the cube immersed is determined by the balance of buoyant force and weight. The buoyant force depends on the apparent weight of the block, which is reduced when the lift moves downward. In the downward motion, the effective gravity acting on the block is reduced to \(g' = g - \frac{g}{2} = \frac{g}{2}\). However, the fraction of the cube immersed remains the same because the buoyant force still exactly balances the cube's weight in the lift, which is now halved. Thus, the fraction of the cube immersed remains unchanged as \(\frac{3}{4}\).