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:

JEE Advanced · 2026 · 17 May 2026 · Paper 2 · Units & Measurement

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

μ_{0}

and

ϵ_{0}

are the permeability and permittivity of free space, respectively, then in this new system of units, the magnitude of one SI unit of

μ_{0} / ϵ_{0}

, is:

Answer: 25

Solution

The dimension of

μ_{0} / ϵ_{0}

[M^{1} L^{2} T^{- 3} A^{- 2}]

.

Using dimensional analysis:

n_{1} u_{1} = n_{2} u_{2}

, where

n_{1} = 1

in SI units.

1 kg\cdotm^{2} \cdots^{- 3} \cdotA^{- 2} = n_{2} [(5 kg) (5 m)^{2} (5 s)^{- 3} (5 A)^{- 2}]

n_{2} = \frac{1}{5 \times 25 \times 5 ^{- 3} \times 5 ^{- 2}} = \frac{1}{5} \times \frac{1}{25} \times 125 \times 25 = 5^{- 1} \times 5^{- 2} \times 5^{3} \times 5^{2} = 5^{2} = 25

JEE Advanced · 2026 · 17 May 2026 · Paper 2 · Numerical answer

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