Question

Capillary tube is a very thin tube. If it is dipped in water, water rises upto height $h=\frac{2T}{r\rho g},$ where r is the radius of tube, $\rho$ is density, and g is acceleration due to gravity. Find dimensional formula of [T]

• A. $M^{-1}{T}^2$
• B. $ML{T}^{-2}$
• C. $ML{T}^{-1}$
• D. $M{T}^{-2}$

Answer 1

The correct option is D $M{T}^{-2}$

$h=\frac{2T}{r\rho g}$
$T=\frac{h\rho rg}{2}=\left[L\right].\left[M{L}^{-3}\right].\left[L\right].\left[L{T}^{-2}\right]=\left[M{T}^{-2}\right]$