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Question

# In English the phrase "tip of the Iceberg" means a small visible fraction of something that is mostly hidden. For a real iceberg what is this fraction, if the density of seawater is 1.03 g/cc and that of ice is 0.92 g/cc ?

A
8.4%
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B
10.6%
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C
20%
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D
85%
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Solution

## The correct option is B 10.6%Given that, Density of seawater, ρsw=1.03 g/cc Density of ice, ρi=0.92 g/cc Let the volume of the iceberg is V and volume of iceberg inside the sea of Vin Volume of iceberg outside the seawater, VO=V−Vin In case of flotation, weight = upthrust i.e. (mg)iceberg=Vinρswg (Vρi)=Vinρsw Vin=Vρiρsw Volume of iceberg outside the seawater, VO=V−Vin VO=V(1−ρiρsw) Fraction of volume outside the water, fout=VOV=(1−ρiρsw) =(1−0.921.03)=0.111.03=0.106 =10.6% Caution:-In upthrust expression only the submerged volume portion is considered.

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