Cube Floating with Displaced Water – Rankers Physics

Fluid Statics: Practice Problem & Solution

A wooden cube is floating in water with some part inside water. When a stone of mass \(4.5\text{ kg}\) is placed on cube then it further sinks by \(5\text{ cm}\). Then side of cube is:
10 cm
30 cm
60 cm
90 cm

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Fluid Statics. Understanding the underlying formula is key to arriving at the correct answer below:

The additional weight of the stone is balanced by the extra buoyant force: \(mg = a^2 \Delta x \rho_w g\). Substituting the values: \(4.5 = a^2 (0.05)(1000)\) gives \(a^2 = 0.09\text{ m}^2\), which yields a side length of \(a = 30\text{ cm}\).

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