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Question

Which of the following sets of quantities have same dimensional formula ?


A

Frequency, angular frequency and angular momentum

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B

Surface tension, stress and spring constant

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C

Acceleration, momentum and retardation

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D

Thermal capacity, specific heat and entropy

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E

Work, energy and torque

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Solution

The correct option is E

Work, energy and torque


Dimensional formula :

The dimensional formula is the statement of a physical quantity in terms of its fundamental unit with suitable dimensions.

For example- electric charge = current ×time

=[A][T] this is the dimensional formula of charge.

The explanation for the correct answer :

W=F.d

=[ML2T-2]

Where W is the work done , F is the applied force and d is the displacement.

Torque(ζ)=F×d

=[ML2T-2]

Where F is the applied force and d is the distance between applied force and axis of rotation.

Energy(E)=mgh(gravitationalpotentialenergy)

=[ML2T-2]

We can also say that work done by a force is stored in the form of systems energy so all three have the same dimensional formula.

Hence, option (E) is correct.


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