(D) The dimensional formula for speed of light $c$ is $[L T^{-1}]$.Given $c = 3 \times 10^8 \,m/s$ ... $(1)$The dimensional formula for acceleration d

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(D) The dimensional formula for speed of light $c$ is $[L T^{-1}]$.Given $c = 3 \times 10^8 \,m/s$ ... $(1)$The dimensional formula for acceleration due to gravity $g$ is $[L T^{-2}]$.Given $g = 10 \,m/s^2$ ... $(2)$To find the unit of time $[T]$, we divide the dimensions of speed by the dimensions of acceleration:$\frac{[L T^{-1}]}{[L T^{-2}]} = [T]$Substituting the given values:$[T] = \frac{3 \times 10^8}{10} = 3 \times 10^7 \,s$Therefore, the unit of time in this system is $3 \times 10^7 \,s$.

Class 11 Physics Units, Dimensions and Measurement Dimensional Analysis, Uses and Limitations

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If speed of light in vacuum $\left(3 \times 10^8 \,m/s\right)$, acceleration due to gravity $\left(10 \,m/s^2\right)$ and mass of electron $\left(9.1 \times 10^{-31} \,kg\right)$ are taken as fundamental physical quantities, then the unit of time in this system is

AP EAMCET 2023 All AP EAMCET

A
$3 \times 10^3 \,s$
B
$5 \times 10^{-19} \,s$
C
$3 \times 10^{19} \,s$
D
$3 \times 10^7 \,s$

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Dimensional Analysis, Uses and Limitations

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If speed of light in vacuum $\left(3 \times 10^8 \,m/s\right)$, acceleration due to gravity $\left(10 \,m/s^2\right)$ and mass of electron $\left(9.1 \times 10^{-31} \,kg\right)$ are taken as fundamental physical quantities, then the unit of time in this system is

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