Question

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

• A. Frequency, angular frequency and angular momentum
• B. Surface tension, stress and spring constant
• C. Acceleration, momentum and retardation
• D. Thermal capacity, specific heat and entropy
• E. Work, energy and torque

Answer 1

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 $\times$time

$=\left[A\right]\left[T\right]$ this is the dimensional formula of charge.

The explanation for the correct answer :

$W=F.d$

$=\left[M{L}^2{T}^{-2}\right]$

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

$Torque\left(\zeta \right)=F\times d$

$=\left[M{L}^2{T}^{-2}\right]$

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

$Energy\left(E\right)=mgh(gravitationalpotentialenergy)$

$=\left[M{L}^2{T}^{-2}\right]$

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.