Choose the correct statements(s):

(a) All quantities may be represented dimensionally in terms of the base quantities.

(b) A base quantity cannot be represented dimensionally in terms of the rest of the base quantities.

(c) The dimensions of a base quantity in other base quantities is always zero.

(d) The dimension of a derived quantity is never zero in any base quantity.

#### Solution

The statements which are correct are:

(a) All quantities may be represented dimensionally in terms of the base quantities.

(b) A base quantity cannot be represented dimensionally in terms of the rest of the base quantities.

(c) The dimensions of a base quantity in other base quantities is always zero.

Statement (d) is not correct because A derived quantity can exist which is dimensionless for example fine structure constant which is given by

\[\alpha = \frac{2\pi e^2}{hc} = \frac{1}{137}\]

\[\text{ where e is the electric charge and c is the speed of light and h is Planks constant . }\]

\[\alpha \text{ is a derived quantity and is dimensionless .}\]