Of the following quantities , which one has the dimensions different from the remaining three?

Options

A. Energy per unit volume
B. Force per unti area
C. Product of voltage and charge per unti volume
D. Angular momentum

Answer

D

Explanation

Dimensions of energy per unit volume
`=("Dimentions of energy")/("Dimensions of volume") = ([ML^(2)T^(-2)])/([L^(3)]) = [ML^(-1)T^(-2)]`
Dimensions of force per unit area
`=("Dimensions of force")/("Dimensions of area") = ([MLT^(-2)])/([L^(2)]) = [ML^(-1)T^(-2)]`
Voltage `xx` Charge/Volume
`=(((W)/(q))xx(it))/(I^(3)) = ((W))/((I^(3))) =([ML^(2)T^(-2)])/([L^(3)]) = [ML^(-1)T^(-2)]`
Angular momentum
`= (r) (p) = (r) (mv) = [L] [M] [LT^(-1)] = [ML^(2)T^(-1)]`
So, dimensions of angular momentum is different from other three.