Question

State which of the following are dimensionally current

(i) Pressure = Energy per unit volume
(ii) Pressure = Momentum × volume × time

CLASS - XI PHYSICS (Physical World & Measurement)

Answer 1

i) Pressure = [ML⁻¹T⁻²]
   Energy per unit volume =  [ML⁻¹T⁻²]

So the first one is correct

ii) Pressure = [ML⁻¹T⁻²]
    Momentum × volume × time = [ML⁴]
So the second one is not correct

Answer 2

This is a quick way of doing it. The right way is to write the dimensional formulas and check them.

Pressure = Force / Area              Energy/volume = Force * distance/ volume
                                                                        = Force / area
So pressure= Energy / volume

ii)
 Momentum * volume * time = (Force * time) * volume * time 
so it is not equal to Force / area