Dimensions of an unknown quantity ,`phi = (ma)/(alpha) log (1 +(alpha l)/(ma))` where `m =` mass, `a=` acceleration and `l = "length"` are

Options

A. `[MLT^(-2)]`
B. `[MT^(-2)]`
C. `[M^(0)LT^(0)]`
D. `[ML^(-3)]`

Answer

C

Explanation

Legarithen has no dimensions
`:. 1 +(alpha t)/(ma) = "dimensionless"`
` :. (alpha t)/(ma) = [M^(0)L^(0)T^(0)]`
`rArr alpha = (ma)/(l) = ([MLT^(-2)])/([L])= [MT^(-2)]`
`:.` Dimensions of `phi = "Demension of" (ma)/(alpha)`
`= ([MLT^(-2)])/([MLT^(-2)]) = [L] = [M^0)LT^(0)`