Properties Of Solids And Liquids Question 102
Question: A metal ball immersed in alcohol weighs $ W _{1} $ at 0°C and $ W _{2} $ at 59°C. The coefficient of cubical expansion of the metal is less than that of alcohol. Assuming that the density of metal is large compared to that of alcohol, it can be shown that [CPMT 1998]
Options:
A) $ W _{1}>W _{2} $
B) $ W _{1}=W _{2} $
C) $ W _{1}<W _{2} $
D) $ W _{2}=(W _{1}/2) $
Show Answer
Answer:
Correct Answer: C
Solution:
As the coefficient of cubical expansion of metal is less as compared to the coefficient of cubical expansion of liquid, we may neglect the expansion of metal ball.
So when the ball is immersed in alcohol at 0ºC, it displaces some volume V of alcohol at 0ºC and has weight W1.
$ \therefore $ W1 = W0 - Vr0g
where W0 = weight of ball in air
Similarly, W2 = W0 - Vr50g
where r0 = density of alcohol at 0ºC and r50 = density of alcohol at 50ºC
As r50 < r0,
therefore W2 > W1 or W1 < W2
