Question

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.

Answer 1

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

$$\begin{gathered} \alpha =\frac{2\pi e^2}{hc}=\frac{1}{137} \\ \mathrm{where}\mathrm{e}\mathrm{is}\mathrm{the}\mathrm{electric}\mathrm{charge}\mathrm{and}\mathrm{c}\mathrm{is}\mathrm{the}\mathrm{speed}\mathrm{of}\mathrm{light}\mathrm{and}\mathrm{h}\mathrm{is}\mathrm{Planks}\mathrm{constant}. \\ \mathrm{\alpha }\mathrm{is}\mathrm{a}\mathrm{derived}\mathrm{quantity}\mathrm{and}\mathrm{is}\mathrm{dimensionless}. \end{gathered}$$