NEET-XII-Physics

01: Introduction to Physics

by HC Verma - page 2
  • #3
    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.
    digAnsr:   a,b,c
    Ans : 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}.``