JEE Advanced 2026 · Paper 2 · Physics Q14

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PhysicsNumerical+4Question 32 of 54

In a new system of units, the units of mass, length, time and current are $5$ kg, $5$ m, $5$ s and $5$ A, respectively. If $\mu_0$ and $\epsilon_0$ are the permeability and permittivity of free space, respectively, then in this new system of units, the magnitude of one SI unit of $\sqrt{\mu_0/\epsilon_0}$ , is:

Your answer

Answer and worked solution

Official answer: 25

$\sqrt{\mu_0/\epsilon_0}$ has the dimensions of resistance:
$[\Omega]=\text{kg m}^2\,\text{s}^{-3}\,\text{A}^{-2}.$
The new unit of resistance is
$\frac{5\cdot5^2}{5^3\cdot5^2}\ \Omega=\frac1{25}\ \Omega.$
So one SI unit (1 Ω) equals 25 new units.

Topics:Dimensional analysis SI units and systems of units

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JEE Advanced 2026 · Paper 2, Physics question 14