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
B
1m
C
4m
D
4.5m

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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