Question

A liquid rises to a height of 5 cm in a glass capillary of radius 0.035 cm. What will be the height of liquid column in a glass capillary of radius 0.05 cm?

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Height\:of\:liquid\:column\:in\:glass\:capillary\:2=2.45\:cm}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Glass \: capillary \: radius( r_{1}) = 0.035 \: cm \\ \\ \tt: \implies Liquid \: rise \: in \: r_{1} \: radius \: capillary( h_{1}) = 5 \: cm \\ \\ \tt: \implies Glass \: capillary \: radius( r_{2}) = 0.05 \: cm \\ \\ \red{\underline \bold{To \: Find :}} \\ \tt: \implies Liquid \: rise \: in \: r_{2} \: radius \: capillary( h_{2}) =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Volume \: of \: capillary \: 1 = Volume \: of \: capillar \: 2 \\ \\ \tt: \implies \pi r_{1}^{2} \: h_{1} = \pi r_{2}^{2} \: h_{2} \\ \\ \tt: \implies \frac{\pi r_{1} ^{2} \: h_{1} }{\pi} = { r_{2} }^{2} \: h_{2} \\ \\ \tt: \implies {0.035}^{2} \times 5 = {0.05}^{2} \times h_{2} \\ \\ \tt: \implies 0.001225 \times 5 = 0.0025 \times h_{2} \\ \\ \tt: \implies h_{2} = \frac{0.001225 \times 5}{0.0025} \\ \\ \green{ \tt: \implies h_{2} =2.45 \: cm}$