Question

Which of the following equations is dimensionally correct?A. pressure = Energy per unit volumeB. pressure = Energy per unit areaC. pressure = Momentum x volume x timeD. pressure = Force x area

Answer 1

Answer ⇒ Option (a). Pressure = Energy per unit volume

Explanation ⇒

Dimensional Formula of the Pressure = ML⁻¹T⁻²

∵ [P] = F/A

= MLT⁻²/L²

= ML⁻¹T⁻²

Let us derive the Dimensional Formula in each option.

Option (A).

Pressure = Energy per unit volume

∴ [P] = ML²T⁻²/L³

[P] = ML⁻¹T⁻²

Since, the dimensional formula derived here is same as the correct Dimensional Formula of the Pressure. Hence, It is dimensionally correct.

Option (B).

Pressure = Energy per unit area

[P] = ML²T⁻²/L²

[P] = ML°T⁻²

Since, the dimensional formula derived here is not same as the correct Dimensional Formula of the Pressure. Hence, It is dimensionally incorrect.

Option (c).

Pressure = Momentum × volume × time

[P] = MLT⁻¹ × L³ × T

[P] = ML⁴T⁰

Since, the dimensional formula derived here is not same as the correct Dimensional Formula of the Pressure. Hence, It is dimensionally incorrect.

Option (d).

Pressure = Force × area

[P] = MLT⁻² × L²

[P] = ML³T⁻²

Since, the dimensional formula derived here is not same as the correct Dimensional Formula of the Pressure. Hence, It is dimensionally incorrect.

From these we can observes that only Option (a) is correct.

Hence, correct answer is option (a).

Hope it helps. :-) 

Answer 2

Option a

Thanks hope it will help you