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JEE MAIN 2021
31-08-2021 S1
Question
If velocity [V], time [T] and force [F] are chosen as the base quantities, the dimensions of the mass will be :
Select the correct option:
A
$\left[\mathrm{FT}^{-1} \mathrm{~V}^{-1}\right]$
B
$\left[\mathrm{FTV}^{-1}\right]$
C
$\left[\mathrm{FT}^2 \mathrm{~V}\right]$
D
$\left[\mathrm{FVT}^{-1}\right]$
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
$\begin{aligned} & {[\mathrm{M}]=\mathrm{K}[\mathrm{F}]^{\mathrm{a}}[\mathrm{T}]^{\mathrm{b}}[\mathrm{V}]^{\mathrm{c}}} \\ & {\left[\mathrm{M}^1\right]=\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2}\right]^{\mathrm{a}}\left[\mathrm{T}^1\right]^{\mathrm{b}}\left[\mathrm{L}^1 \mathrm{~T}^{-1}\right]^{\mathrm{c}}} \\ & \mathrm{a}=1, \mathrm{~b}=1, \mathrm{c}=-1 \\ & \therefore[\mathrm{M}]=\left[\mathrm{FTV}^{-1}\right]\end{aligned}$
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