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 $\gamma _{Fe}$ and that of mercury is $\gamma _{Hg}$, then the ratio $k _1 / k _2$ can be expressed as
(2001, 2M)
(a) $\frac{1+60 \gamma _{Fe}}{1+60 \gamma _{Hg}}$
(b) $\frac{1-60 \gamma _{Fe}}{1+60 \gamma _{Hg}}$
(c) $\frac{1+60 \gamma _{Fe}}{1-60 \gamma _{Hg}}$
(d) $\frac{1+60 \gamma _{Hg}}{1+60 \gamma _{Fe}}$
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Answer:
Correct Answer: 9. (a)
Solution:
- $h=\frac{2 \sigma \cos \theta}{r \rho g}$
(a) $\rightarrow h \propto \frac{1}{r}$
(b) $h$ depends upon $\sigma$.
(c) If lift is going up with constant acceleration.
$$ g _{\text {eff }}=(g+a) \Rightarrow h=\frac{2 \sigma \cos \theta}{r \rho(g+a)} $$
It means $h$ decreases.
(d) $h$ is proportional to $\cos \theta$.
