Question

If density D, velocity V and acceleration A are taken as fundamental quantities the dimensions of mass are
(A) DºV2A-1
(B) DºVA-1
(C) DV6A-3
(D) DSV A-3

Answer 1

Answer:

I think the answer is c I hope you understand

Answer 2

The Main Answer is: (c) $DV^{6}A^{-3}$

Given: Fundamental quantities are Density (D)

                                                           Velocity (V)

                                                           Acceleration (A)

To Find: Dimensions of MASS

Solution:

This question uses the concept of 'Units and Physical Dimensions'

As opposed to normal practice, in this question, the fundamental units are changed and are not Mass, Length and Time, but Density, Velocity, and Acceleration.

In such a case, one would normally try to find a relation between the quantity whose dimensions we have to find and the given fundamental quantities.

But, in this case, there seems to be no direct relationship between the given quantities and mass.

Therefore, we will have to match the units of mass and a relation of the fundamental quantities by 'hit-and-trial'.

Units of Density = kg/m³

Units of Velocity = m/sec

Units of Acceleration = m/sec²

Units of mass = kg

∴ We have to formulate a relation between the fundamental quantities such that their units result in only 'kg'.

By hit and trial, we conclude that $(\frac{kg}{m^{3} } )(\frac{m}{sec } )^{6} (\frac{m}{sec^{2} } )^{-3}$ is the right relation.

Here, we get, $(\frac{kg}{m^{3} } )(\frac{m^{6}}{sec^{6} } ) (\frac{sec^{6}}{m^{3} } )$

                     = kg = units of mass

This relation translates to $DV^{6}A^{-3}$

Therefore, the correct answer is $DV^{6}A^{-3}$

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