Question

taking velocity ,time and force as the fundamental quantities,find the dimensions of mass

Answer 1

Answer:

Therefore,dimension of mass(M) = [F T $V^{-1}$]

Explanation:

We know that,

Force = Mass x Acceleration

Mass =  $\frac{Force}{Acceleration}$

$or, Mass = \frac{Force}{\frac{Velocity}{Time} }$

$or, Mass(M) = \frac{Force(F)}{\frac{Velocity(V)}{Time(T)} }$

M = F T $V^{-1}$

Therefore,dimension of mass(M) = [FT $V^{-1}$]

Answer 2

Answer:    $[M]=[FTV^{-1}]$

Explanation: We know, [Velocity] = $[LT^{-1}]$

[Time] = $[T]$

[Force] = $[MLT^{-2}]$

[Mass] = $[M]$

So, out of velocity, time and mass, only force has mass. Therefore,

$[Mass]=\frac{[Force]}{[LT^{-2} ]}$

And $[LT^{-2} ]=\frac{[Velocity]}{[Time]}$,

Therefore, Mass = $\frac{Force * Velocity}{Time}$, $[M]=[FTV^{-1}]$

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