If velocity

Question:

If velocity $[\mathrm{V}]$, time $[\mathrm{T}]$ and force $[\mathrm{F}]$ are chosen as the base quantities, the dimensions of the mass will he.

  1. $\left[\mathrm{FT}^{-1} \mathrm{~V}^{-1}\right]$

  2. $\left[\mathrm{FTV}^{-1}\right]$

  3. $\left[\mathrm{FT}^{2} \mathrm{~V}\right]$

  4. $\left[\mathrm{FVT}^{-1}\right]$


Correct Option: , 2

Solution:

${[\mathrm{M}]=\mathrm{K}[\mathrm{F}]^{\mathrm{a}}[\mathrm{T}]^{\mathrm{b}}[\mathrm{V}]^{\mathrm{c}} }$

${\left[\mathrm{M}^{\mathrm{l}}\right]=\left[\mathrm{M}^{\mathrm{l}} \mathrm{L}^{\mathrm{1}} \mathrm{T}^{-2}\right]^{\mathrm{a}}\left[\mathrm{T}^{\mathrm{l}}\right]^{\mathrm{b}}\left[\mathrm{L}^{\mathrm{l}} \mathrm{T}^{-1}\right]^{\mathrm{c}} }$

$\mathrm{a}=1, \mathrm{~b}=1, \mathrm{c}=-1$

$\therefore[\mathrm{M}]=\left[\mathrm{FTV}^{-1}\right]$

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