If speed of light in vacuum $\left(3 \times 10^8 \mathrm{~ms}^{-1}\right)$, acceleration due to gravity…
If speed of light in vacuum $\left(3 \times 10^8 \mathrm{~ms}^{-1}\right)$, acceleration due to gravity $\left(10 \mathrm{~ms}^{-2}\right)$ and mass of electron $\left(9.1 \times 10^{-31} \mathrm{~kg}\right)$ are taken as fundamental physical quantities, then the unit of time in this system is
$3 \times 10^3 \mathrm{~s}$
$5 \times 10^{-19} \mathrm{~s}$
$3 \times 10^{19} \mathrm{~s}$
$3 \times 10^7 \mathrm{~s}$
Solution
Speed of light, $\left[\mathrm{L} \mathrm{T}^{-1}\right]=3 \times 10^8 \mathrm{~m} / \mathrm{s}$ ... (1) acceleration due to gravity, $\left[\mathrm{L} \mathrm{T}^{-2}\right]=10 \mathrm{~m} / \mathrm{s}^{-2}$ ... (2)
Divide equation (1) by (2), we have
$\frac{\left[\mathrm{L} \mathrm{T}^{-1}\right]}{\left[\mathrm{LT}^{-2}\right]}=\frac{3 \times 10^8}{10} \Rightarrow[\mathrm{T}]=3 \times 10^7 \mathrm{~s}$