Speed of light in vacuum is given by 3 × 108 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

Question

Speed of light in vacuum is given by 3 × 108 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 × 108 (B) 6 × 108 (C) 1.5 × 108 (D) 9 × 108

Tardigrade Admin · Accepted Answer

As n1 u1=n2 u2 ⇒ n2=((u1/u2))n1=((L1T-11/L2T-12))(n1) =((1/2)×4)(3×108)=6×108

Q. Speed of light in vacuum is given by $3 \times 1 0^{8} m s^{- 1}$ in $M K S$ 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

$3 \times 1 0^{8}$

$6 \times 1 0^{8}$

$1.5 \times 1 0^{8}$

$9 \times 1 0^{8}$

As $n_{1} u_{1} = n_{2} u_{2}$
$\Rightarrow n_{2} = (\frac{u _{1}}{u _{2}}) n_{1} = (\frac{L _{1} T _{1}^{- 1}}{L _{2} T _{2}^{- 1}}) (n_{1})$
$= (\frac{1}{2} \times 4) (3 \times 1 0^{8}) = 6 \times 1 0^{8}$

Q. Speed of light in vacuum is given by 3×108ms−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

3×108

6×108

1.5×108

9×108