Question
If force $$\left( F \right),$$ velocity $$\left( V \right)$$ and time $$\left( T \right)$$ are taken as fundamental units, then the dimensions of mass are
A.
$$\left[ {Fv{T^{ - 1}}} \right]$$
B.
$$\left[ {Fv{T^{ - 2}}} \right]$$
C.
$$\left[ {F{v^{ - 1}}{T^{ - 1}}} \right]$$
D.
$$\left[ {F{v^{ - 1}}T} \right]$$
Answer :
$$\left[ {F{v^{ - 1}}T} \right]$$
Solution :
$$\eqalign{
& {\text{We know that}} \cr
& F = ma \cr
& \Rightarrow F = \frac{{mv}}{t} \cr
& \Rightarrow m = \frac{{Ft}}{v} \cr
& \left[ M \right] = \frac{{\left[ F \right]\left[ T \right]}}{{\left[ v \right]}} = \left[ {F{v^{ - 1}}T} \right] \cr} $$