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Question

A large block of ice $$5m$$ thick has a vertical hole drilled in it and is floating in a lake. The minimum length of the rope required to draw a bucketfulll of water through the hole is (density of ice=$$900km/m^3$$)


A
0.5m
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B
1m
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C
4m
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D
4.5m
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Solution

The correct option is A $$0.5m$$

Area of ice, $$A$$

Weight of ice, $$W={{\rho }_{ice}}gL$$

Weight of water, $$W={{\rho }_{water}}gh$$

From condition of equilibrium.

Weight of water = weight of ice

$$ {{\rho }_{ice}}gL={{\rho }_{water}}gh $$

$$ h=\dfrac{{{\rho }_{ice}}}{{{\rho }_{water}}}L=\dfrac{900}{1000}\times 5=4.5\,m $$

Required length of rope, $$5-4.5\,=0.5\,m$$

Hence, length of bucket required to draw water is $$\left( 5-4.5 \right)\,=0.5\,m$$.


Physics

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