(a) `K = m^2 upsilon^3 = (kg)^2(ms^(-1))^3`
`=kg^2m^3 s^(-3)`
(b) `K =(1)/(2)m upsilon^2 = kg (ms^(-1))^2 = kg m^2 s^(-2)`
(c ) `K = ma =kg(ms^(-2)) = kg ms^(-2)`
(d) `K = (3)/(16) m upsilon^2 = kg (ms^(-1))^2 = kg m^2 s^(-2)`
(e ) `K =(1)/(2)m upsilon^2 +ma = kg(ms^(-1))^2 + kg(ms^(-2))`
`=kg m^2 s^(-2) +kg ms^(-2)`
The two parts having different dimensions
cannot be added.
Clearly, on the basis of dimensilonal arguments,
(a) ,(c ) and (e ) are ruled out. Choices (b) and (d) are
correct. The dimensional argument does not
distinguish between (b) and (d). From actual
derivation in unit 4, we shall find the choice (b) is correct.