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Question

A sphere of diameter 7 cm and mass 266.5 gm floats in a bath a liquid As the temperature is raised, the sphere just begins to sink at a temperature 350C If the density of a liuid at 0C is 1.527 gm/cc, Then neglecting the expansion of the sphere, the coefficient of cubical expansion of the liquid is :

A
8.048×104per0C
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B
8.048×105per0C
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C
8.486×105per0C
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D
8.486×103per0C
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Solution

The correct option is A 8.048×104per0C
Let coeff of expansion of liquid be r
The sphere has mass =266.5 and a volume =43π(d2)3 where d=7cm
so density of sphere =p=mv=266.543π(d2)3=1.484glcc
Due to thermal expansion,the density of liquid decreases which is :-
P=P0(γΔT)
where ΔT=35K
P0:Density of liquid at 0oC
The sphere begins to ink in liquid when its density equals to density of liquid
=P0(1γΔ)=1.484
=1.527(1γ×35)=1.484
35γ=(1.4841.527)
γ=8.05×104K1

1068304_1166148_ans_83e6bd23925041a18333d67c8e7f920b.png

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