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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.

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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 $\alpha =\frac{2\pi {e}^{2}}{hc}=\frac{1}{137}\phantom{\rule{0ex}{0ex}}\mathrm{where}\mathrm{e}\mathrm{is}\mathrm{the}\mathrm{electric}\mathrm{charge}\mathrm{and}\mathrm{c}\mathrm{is}\mathrm{the}\mathrm{speed}\mathrm{of}\mathrm{light}\mathrm{and}\mathrm{h}\mathrm{is}\mathrm{Planks}\mathrm{constant}.\phantom{\rule{0ex}{0ex}}\mathrm{\alpha }\mathrm{is}\mathrm{a}\mathrm{derived}\mathrm{quantity}\mathrm{and}\mathrm{is}\mathrm{dimensionless}.$

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