SATHEE: Properties of Matter 4 Question 7

Properties of Matter 4 Question 7

9. When a block of iron floats in mercury at $0^{\circ} C$ , fraction $k_{1}$ of its volume is submerged, while at the temperature $60^{\circ} C$ , a fraction $k_{2}$ is seen to be submerged. If the coefficient of volume expansion of iron is $γ_{F e}$ and that of mercury is $γ_{H g}$ , then the ratio $k_{1} / k_{2}$ can be expressed as

(2001, 2M)

(a) $\frac{1 + 60 γ_{F e}}{1 + 60 γ_{H g}}$

(b) $\frac{1 - 60 γ_{F e}}{1 + 60 γ_{H g}}$

(d) $\frac{1 + 60 γ_{H g}}{1 + 60 γ_{F e}}$

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Answer:

Correct Answer: 9. (a)

Solution:

$h = \frac{2 σ \cos θ}{r ρ g}$

(a) $\to h \propto \frac{1}{r}$

(b) $h$ depends upon $σ$ .

$g_{eff} = (g + a) \Rightarrow h = \frac{2 σ \cos θ}{r ρ (g + a)}$

It means $h$ decreases.

(d) $h$ is proportional to $\cos θ$ .

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Properties of Matter 4 Question 7

9. When a block of iron floats in mercury at 0∘C, fraction k1 of its volume is submerged, while at the temperature 60∘C, a fraction k2 is seen to be submerged. If the coefficient of volume expansion of iron is γFe and that of mercury is γHg, then the ratio k1/k2 can be expressed as

Answer:

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