Of the following quantities which one has the dimensions different from the remaining three?
(i) Energy density
(ii) Force per unit area
(iii) Product of charge per unit volume and voltage
(iv) Angular momentum per unit mass

Options

A. (i)
B. (ii)
C. (iii)
D. (iv)

Answer

D

Explanation

`"Energy density"= ("Energy")/("Volume")= ([ML^(2)T^(-2)])/([L^(3)])= [ML^(-1)T^(-2)]`
`("Force")/("Area")= ([MLT^(-2)])/([L^(2)])= [ML^(-1)T^(-2)]`
`("Charge")/("Volume") xx "Voltage"= ("Charge")/("Volume") xx ("Work")/("Charge")= ("work")/("volume")= ([ML^(2)T^(-2)])/([L^(3)])= [ML^(-1)T^(-2)]`
`("Angular momentum")/("mass")= ([ML^(2)T^(-1)])/([M])= [M^(0)L^(2)T^(-1)]`
Therefore, dimensions of (iv) is different.