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The physical quantities not having same dimensions are

Asked in AIEEE 2003 · Pairs with the same dimensions

(1) torque and work
(2) momentum and Planck's constant
(3) stress and Young's modulus
(4) speed and (μ₀ε₀)^-1/2

Answer: (2) momentum and Planck's constant

Step-by-step solution

Momentum is [MLT⁻¹].

Planck's constant is [ML²T⁻¹].

They differ by one power of length, so this is the odd pair.

The other three pairs each match exactly.

Why the other options are wrong

(1) comes from both are [ML²T⁻²]
(3) comes from both are [ML⁻¹T⁻²], since strain is dimensionless
(4) comes from both are [LT⁻¹], the second being the speed of light

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