JEE MAIN - Physics (2021 - 27th August Morning Shift - No. 2)
Which of the following is not a dimensionless quantity?
Relative magnetic permeability ($$\mu$$r)
Power factor
Permeability of free space ($$\mu$$0)
Quality factor
Explanation
[$$\mu$$r] = 1 as $$\mu$$r = $${\mu \over {{\mu _m}}}$$
[power factor (cos $$\phi$$)] = 1
$${\mu _0} = {{{B_0}} \over H}$$ (unit = NA$$-$$2) : Not dimensionless
[$$\mu$$0] = [MLT$$-$$2A$$-$$2]
quality factor $$(Q) = {{Energy\,stored} \over {Energy\,dissipated\,per\,cycle}}$$
So Q is unitless & dimensionless.
[power factor (cos $$\phi$$)] = 1
$${\mu _0} = {{{B_0}} \over H}$$ (unit = NA$$-$$2) : Not dimensionless
[$$\mu$$0] = [MLT$$-$$2A$$-$$2]
quality factor $$(Q) = {{Energy\,stored} \over {Energy\,dissipated\,per\,cycle}}$$
So Q is unitless & dimensionless.
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