Test if the following equation is dimensionally correct: `h= ((sS cos theta)/(r p g))` where h= height, S= surface tension, p= density, r=radius, and g= acceleration due to gravity.

Options

A. `s = 1/2 at^2`
B. `v = sqrt(T//m)`
C. `t = (2h)/g`
D. `a = (v^2)/r`

Answer

C

Explanation

`a . S = 1/2 at^2 , [L] = [LT^(-2)][T^2] = [L]`
`b. V = sqrt(T/m)`
`[LT^(-1)] = [(MLT^(-2))/(ML^(-1))]^(1//2) = [LT^(-1)]`
`c = t = (2h)/g , [t] = [T]`
`[(2h)/(g)] = [(L)/(LT^(-2))] = T^2 ` not equal to [T]
`d . A = (V^2)/r`
`implies [LT^(-2)] = ([LT^(-1)]^(2))/([L]) = [LT^(-2)]`