Dimensionsal methods provide three major advantages in verification , deviation , and changing the system of units . Any empirical formula that is derived based on this method has to be verified and propportionality constants found by experimental means . The presence or absence of certain factors - non dimensional constants or variables - cannot be identified by this method . So every dimensionally correct relation cannot be taken as perfectly correct.
The time period of oscillation of a drop depends on surface tension `sigma` , density of the liquid `rho` , and radius ` r ` . The relation is

Options

A. ` sqrt (( rho r^(2))/( sigma))`
B. ` sqrt (( r^(2))/( rho sigma))`
C. ` sqrt (( r^(3) rho)/( sigma))`
D. ` sqrt (( rho sigma)/( r^(3)))`

Answer

C

Explanation

Let `T prop sigma ^(a) rho^(b) r^(c )`
`M^(0) L^(0) T = (MT^(-2))^(a) (ML^(-3))^(b) L^(c )`
Equating the powers of `M: 0 = a + b rArr b = -a`
`L : 0 = -3b + c rArr c = 3b`
`T : 1 = -2a rArr a = -(1)/(2), b = (1)/(2) , c = (3)/(2) rArr T = k sqrt((r^(3)rho)/(sigma))`