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A large block of ice 5 m thick has a vertical hole drilled in it and is floating in a lake. The minimum length of the rope required to draw a bucketful of water through the hole is $\frac{x}{4}$ m. The value of $x$ is ____ (density of ice = 900 kg/m³)

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answer is 2.

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Detailed Solution

The fraction of ice block above water level is given by

$\frac{V_{out}}{V} = 1 - \frac{ρ_{ice}}{ρ_{water}} = 1 - \frac{900}{100} = 0.1$

$\Rightarrow \frac{A h_{o u t}}{A h} = 0.1 \Rightarrow h_{out} = 0.1 \times 5 = 0.5 m$

Hence, minimum length of the rope required is 0.5 m = 2/4 m

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