Question

Calculate the density of a liquid contained in a thin tube of area of cross- section 0.4 mm2

. If the length of the

liquid is 8 cm and its mass is 0.2 gm​

Answer 1

Given:-

• Cross - Sectional area of tube is 0.4mm².
• Length of liquid in tube is 6cm.
• Mass of liquid is 0.2g.

To Find:-

• The density of the liquid.

Formula Used:-

We know that density is equal to mass by volume.

$\large\orange{\underline{\boxed{\green{\tt{\dag Density(\rho) =\dfrac{Mass(m)}{Volume (V)}}}}}}$

Also , volume is equal to :

$\large\orange{\underline{\boxed{\green{\tt{\dag Volume (V)=Area(A)\:\:\times\:\: Height (h) }}}}}$

Calculation:-

Given cross - Sectional area is 0.4mm² . So , firstly covert it to cm .

We know 1cm = 10mm

➥ 0.4mm² = 0.4/100cm² = 0.004cm².

Now , lets find its volume ,

Here , length = 6cm.

Putting the values as in above mentioned , we have,

$\tt:\implies Volume=Cross\:Sec.\:Area\times\:lenght$

$\tt:\implies Volume = 0.004cm^2\times6cm$

$\tt{\underline{\boxed{\red{\tt{\longmapsto Volume\:\:=\:\:0.024cm^3}}}}}$

$\blue{\tt Hence\:the\: Volume\:is\:0.024cm^3.}$

________________________________________

$\pink{\tt Putting \:the\:values\:in\: above\: formula\:stated:-}$

$\tt:\implies Density=\dfrac{Mass}{Volume}$

$\tt:\implies \rho = \dfrac{0.2g}{0.024cm^3}$

$\tt:\implies \rho =\dfrac{\cancel{2}\times 100\cancel{0}}{\cancel{24}^{12}\times\cancel{10}}$

$\tt{\underline{\boxed{\red{\tt{\longmapsto Density\:(\rho)\:\:\:\:=\:\:\:\:8.33g/cm^3\approx 8g/cm^3}}}}}$

$\underline{\blue{\bf{\leadsto Hence\:the\:density\:of\: liquid\:is\:8.33g/cm^3.}}}$