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A cubical block of ice floating in water...

A cubical block of ice floating in water has to suport metal piece weighing 0.5 kg. What can be the minimum edge of the block so that it does not sink in water/ specific gravity of ice=0.9.

Text Solution

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The correct Answer is:
A, C
`P_(ice)=0.9gm/cc`
m=5kg
let xrarr minimum edge of the ice block in cm.
s, `mg=W_(ice)=U`
where U =upward thrust
`rarr 0.5xg+x^3xxrho_(ice)xxg=x^3xxrho_wxxg`
` [becauyse liquid displaced `-x^3`]
`rarr 0.5xx10^3xxx^3x(0.9)=x^3xx1`
`rarr x^3xx(0.1)=(0.5)xx10^3`
`-x^3=5xx10^3`
`rarr x=17.09cm`
`=17cm`
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