Units and Measurements Part 1

As we know that, the dimensional formula of
density [D]=[ML−3T0]
Since, dimensional formula of force
[F]=[MLT−2]
Dimensional formula of length
[L]=[M0L1T0]
Dimensional formula of time
[T]‌‌=[M0L0T1]
∴‌‌[D]‌‌=[F]a[Lb[T]c
⇒‌‌[ML−3T0]‌‌=[ML−2]a
‌[M0L1T0]b[M0L0T1]c
‌‌=[MaLa+bT−2a+c]
Comparing powers of dimensions on both sides, we get
ca=1
a+b=−3
⇒‌‌b=−3−1=−4
and ‌‌−2a+c=0
‌‌c=2a
⇒‌‌c=2×1=2
∴ Dimensional formula of density will be
[F1L−4T2].