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

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 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:

Q. A body is floating in a liquid. At two temperatures

t_{1}^{\circ} C

and

t_{2}^{\circ} C

of the liquid, fractions

f_{1}

and

f_{2}

of the volumes of the body remain immersed in the liquid. Coefficient of volume expansion of the liquid is:

Join BYJU'S Learning Program

A solid whose volume does not change with temperature floats in a liquid. For two different temperatures t1 and t2 of the liquid, fractions f1 and f2 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 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