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Question

A metal ball is immersed in alcohol weighing$\ fracW1 at 0°C \$and W2 at 50°C. The coefficient of cubical expansion of the metal is less than that of alcohol. Assuming that density of metal is large compared to that of alcohol, it can be shown


A
W1>W2
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B
W1=W2
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C
W1<W2
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D
Relation between W1 & W2 can not be established.
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Solution

The correct option is A W1>W2
Let volume and density of ball at 0°C be V1 & ρ1 respectively and at 50°C be V2 & ρ2 respectively.
As in both the case, ball is completely immersed in alcohol , so volume displaced of liquid will be same as the volume of ball.
By Law of Buoyancy,
W1=V1ρ1g & W2=V2ρ2g
W1W2=V1ρ1V2ρ2
Now, ρ1 >ρ2
as volume of ball increases. Because of expansion of alcohol, volume of alcohol increases while mass remain same so density of alcohol decreases. Though V2>V1 , but as the coefficient of cubical expansion of the metal is less than that of alcohol, its effect can be neglected compared to effect of liquid and it can be considered as V2V1.
Therefore W1W2>1 W1>W2

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