If velocity V time T and force F are chosen as the base quantities, the dimensions of the mass will be :

If velocity V time T and force F are chosen as the base quantities, the dimensions of the mass will be :
  1. FVT-1
  2. FT-1V-1
  3. FT2 V
  4. FTV-1

Solution

[M]1=[V]a[T]b[F]c
[M]1=LT-1a[T]bMLT-2c
[M]1=[M]c[L]a+c[T]-a+b-2c
Thus,

c=1,a+c=0 andb-a-2c=0⇒a=-1⇒b=-1+2=1
Thus, [M]=[V]-1[ T]1[ F]1

Asked in: JEE Main 2021 (31 Aug Shift 2)

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