Question

The fundamental physical quantities that have same dimensions in the dimensional formulae of torque and angular momentum are
A. mass, time
B. time, lengthC. mass, length
D. time, mole

Answer 1

Answer ⇒ Option (c). Mas and Length.

Solution ⇒

The Dimensional Formula of the Torque = ML²T⁻².

∵ Torque = Force × Displacement.

∴ [T] = MLT⁻² . L

[T] = ML²T⁻²

The Dimensional Formula of the Angular Momentum = ML²T⁻¹

Angular Momentum = M.I. × Angular Velocity

= ML²T⁻¹

Now, we can see that Dimensions of the mass (M) , length(L) in powers are same in both the Torque and Angular Momentum.

Thus, Option (C). mass and time is correct.

Although the fundamental unit, time is present in both the Quantities but its powers are not same in both the quantities.

Hope it helps. :-)

Answer 2

Option c

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