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.
If `alpha` kilogram , `beta` meter , and `gamma` second are the fundamental units , `1 cal` can be expressed in new units as `[ 1 cal = 4.2 J]`

Options

A. `alpha^(-1) beta ^(2) gamma`
B. `alpha^(-1) beta^(-2) gamma`
C. ` 4.2 alpha^(-1) beta`
D. ` 4.2 alpha^(-1) beta^(-2) gamma^(2)`

Answer

D

Explanation

` 1 cal = 4.2 J = 4.2 kg m^(2) s^(-2) = n_(2) (alpha kg) (beta m)^(2) (gamma s)^(-2)`
`rArr n_(2) = 4.2 alpha ^(-1) beta^(-2) gamma^(2)`
So , `1 cal = (4.2 alpha^(-1) beta^(-2) gamma^(2))` new units