Question

check the dimensional accuracy of t equals to rh row g upon 2 cos theta where t is surface tension, r in radius of the tube , row is density and , theta is angle of contact

Answer 1

you mean, we have to check dimension accuracy of ,

$\bf{T=\frac{r\rho gh}{2cos\theta}}$.

where T is surface tension,

r is radius of the tube,

$\rho$ is density of liquid,

h is height of liquid in the capillary tube.

and $\theta$ is angle of contact.

we know, dimension of T = [MT-²]

dimension of r = [L]

dimension of $\rho$ = [ML-³]

dimension of h = [L]

dimension of g = [LT-²]

so, LHS = [MT-²]

RHS = [L][ML-³][LT-²][L]

= [MT-²]

here LHS = RHS

so, given formula is dimensionally correct.

Answer 2

Explanation:

you mean, we have to check dimensional accuracy of - T= rhpg / 2cos theta

.

where T is surface tension,

r is radius of the tube,

\rhoρ is density of liquid,

h is height of liquid in the capillary tube.

and \thetaθ is angle of contact.

we know, dimension of T = [MT-²]

dimension of r = [L]

dimension of \rhoρ = [ML-³]

dimension of h = [L]

dimension of g = [LT-²]

so, LHS = [MT-²]

RHS = [L][ML-³][LT-²][L]

= [MT-²]

here LHS = RHS

so, given formula is dimensionally correct