A solid whose volume does not change with temperature floats in a liquid. For two different temperatures $t_{1}$ and $t_{2}$ of the liquid, fractions $f_{1}$ and $f_{2}$ of the volume of the solid remain submerged in the liquid. The coefficient of volume expansion of the liquid is equal to

\frac{f_{1} - f_{2}}{f_{2} t_{1} - f_{1} t_{2}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

\frac{f_{1} - f_{2}}{f_{1} t_{1} - f_{2} t_{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{f_{1} + f_{2}}{f_{2} t_{1} + f_{1} t_{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{f_{1} + f_{2}}{f_{1} t_{1} + f_{2} t_{2}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{f_{1} - f_{2}}{f_{2} t_{1} - f_{1} t_{2}}$
As with the rise in temperature, the liquid undergoes volume expansion therefore the fraction of solid submerged in liquid increases.
Fraction of solid submerged at ${t_{1}}^{\circ} C = f_{1}$ = Volume of displaced liquid $= V_{0} (1 + γ t_{1}) \dots \dots (i)$ and fraction of solid submerged at ${t_{2}}^{\circ} C = f_{2}$ = Volume of displaced liquid $= V_{0} (1 + γ t_{2}) \dots \dots (i i)$
From (i) and (ii) $\frac{f_{1}}{f_{2}} = \frac{1 + γ t_{1}}{1 + γ t_{2}}$ $\Rightarrow$ $γ = \frac{f_{1} - f_{2}}{f_{2} t_{1} - f_{1} t_{2}}$

Suggest Corrections

Similar questions

A solid whose volume does not change with temperature floats in a liquid. For two different temperatures $t_{1} a n d t_{2}$ of the liquid, fractions $f_{1} a n d f_{2}$ of the volume of the solid remain submerged in the liquid. The coefficient of volume expansion of the liquid is equal to

Q. A solid whose volume does not change with temperature floats in a liquid. For two different temperatures

t_{1}

and

t_{2}

of the liquid, fractions

f_{1}

and

f_{2}

of the volume of the solid remain submerged in the liquid. The coefficient of volume expansion of the liquid is equal to

A solid whose volume does not change with temperature floats in liquid at two different temperatures $t_{1}^{0} C$ and $t_{2}^{0} C$ of the liquid. Fractions of the volume of the solid remain submerged are $f_{1}$ and $f_{2}$ respectively. The coefficient of absolute expansion of the liquid is equal to: