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

${\mathfrak{\underline{\purple{\:\:\: Given:-\:\:\:}}}}$

$\:\:\:\:\bullet\:\:\:\sf{Glass \: capillary \: radius( r_{1}) = 0.035 \: cm }$

$\:\:\:\:\bullet\:\:\:\sf{Liquid \: rise \: in \: r_{1} \: radius \: capillary( h_{1}) = 5 \: cm}$

$\:\:\:\:\bullet\:\:\:\sf{Glass \: capillary \: radius( r_{2}) = 0.05 \: cm }$

${\mathfrak{\underline{\purple{\:\:\:To \:Find:-\:\:\:}}}}$

$\:\:\:\:\bullet\:\:\:\sf{ Liquid \: rise \: in \: r_{2} \: radius \: capillary( h_{2}) =?}$

${\mathfrak{\underline{\purple{\:\:\: Solution:-\:\:\:}}}}$

★ Volume of capillary 1 = Volume of capillar 2

$\dashrightarrow\:\: \sf{ \pi r_{1}^{2} \: h_{1} = \pi r_{2}^{2} \: h_{2}}$

$\dashrightarrow\:\: \sf{ \dfrac{\pi r_{1} ^{2} \: h_{1} }{\pi} = { r_{2} }^{2} \: h_{2}}$

$\dashrightarrow\:\: \sf{{0.035}^{2} \times 5 = {0.05}^{2} \times h_{2}}$

$\dashrightarrow\:\: \sf{0.001225 \times 5 = 0.0025 \times h_{2}}$

$\dashrightarrow\:\: \sf{h_{2} = \dfrac{0.001225 \times 5}{0.0025}}$

$\dashrightarrow\:\: \sf{\dfrac{0.006125}{0.0025}}$

$\dashrightarrow\:\: \sf{h_{2} =2.45 \: cm}$

$\therefore\:\bf{Height\: of\: the\:liquid\: column\:is\:2.45 \: cm}$