The coefficient of volume expansion of mercury is $20$ times the coefficient of linear expansion of glass. Find the volume of mercury that must be poured into a glass vessel of volume V so that the volume above mercury may remain constant at all temperature

$\frac{V}{10}$

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$\frac{3 V}{10}$

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$\frac{5 V}{10}$

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$\frac{3 V}{20}$

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Solution

The correct option is D
$\frac{3 V}{20}$

$γ H g = 20 α_{g}$
from given condition, $V_{h g} \times γ H g = V \times γ_{v e s s e l}$
$V_{H g} = \frac{V \times 3 α_{g}}{20 α_{g}} = \frac{3 V}{20}$

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The coefficient of volume expansion of mercury is $20 t i m e s$ the coefficient of linear expansion of glass. If the volume of mercury that must be poured into a glass vessel of volume $V$ so that the volume above mercury may remain constant at all temperature is $\frac{x V}{20} .$ Find $x .$

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The coefficient of volume expansion of mercury is 20 times the coefficient of linear expansion of glass. Find the volume of mercury that must be poured into a glass vessel of volume V so that the volume above mercury may remain constant at all temperature

The correct option is D 3V20 γHg=20αg from given condition, Vhg×γHg=V×γvessel VHg=V×3αg20αg=3V20

The coefficient of volume expansion of mercury is $20$ times the coefficient of linear expansion of glass. Find the volume of mercury that must be poured into a glass vessel of volume V so that the volume above mercury may remain constant at all temperature

The correct option is D
$\frac{3 V}{20}$

$γ H g = 20 α_{g}$
from given condition, $V_{h g} \times γ H g = V \times γ_{v e s s e l}$
$V_{H g} = \frac{V \times 3 α_{g}}{20 α_{g}} = \frac{3 V}{20}$