Question

Speed of light in vacuum is given by $3 \times 10^8\, m\, s^{-1}$ in $MKS$ system. If in a new system, the unit of length and time is increased by a factor of $2$ and $4$, respectively, then the numerical value of speed of light in this new system will be

• A. $3 \times 10^8$
• B. $6 \times 10^8$
• C. $1.5 \times 10^8$
• D. $9 \times 10^8$

Answer 1

Answer: (B)

$6 \times 10^8$

Answer 2

As $n_1\,u_1=n_2\,u_2$ $\Rightarrow n_{2}=\left(\frac{u_{1}}{u_{2}}\right)n_{1}=\left(\frac{L_{1}T^{-1}_{1}}{L_{2}T^{-1}_{2}}\right)\left(n_{1}\right)$ $=\left(\frac{1}{2}\times4\right)\left(3\times10^{8}\right)=6\times10^{8}$