NEET-XII-Physics
01: Introduction to Physics
- #3Choose 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.digAnsr: a,b,cAns : 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}.``