A light cylindrical tube T of length l and radius r containing air is inverted in water (density d 1 ). One end of the tube is open and the other is closed. A block B of density d 2 d 1 is kept on the tube as shown in the figure. The tube stays in equilibrium in the position shown. Find the volume of B . Density of the air is negligible as compared with the density of water :

Question

A light cylindrical tube T of length l and radius r containing air is inverted in water (density d 1 ). One end of the tube is open and the other is closed. A block B of density d 2 > d 1 is kept on the tube as shown in the figure. The tube stays in equilibrium in the position shown. Find the volume of B . Density of the air is negligible as compared with the density of water :, v = d 1 d 2 - d 1 p r 2 l 3, v = d 2 d 2 - d 1 p r 2 l 3, v = d 1 d 1 - d 2 p r 2 l 3, v = d 1 d 2 p r 2 l 3

MARKS App · Accepted Answer

The free body diagram of block + tube inclusive of water is as shown. Since the block + tube system shown in figure is in equilibrium. ∴ Net weight of system = buoyant fore Let v be the volume of the block, then d 2 v g = v + π r 2 l 3 d 1 g ⇒ d 2 - d 1 v = π r 2 l 3 or v = d 1 d 2 - d 1 π r 2 l 3

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