Let `[in_(0)]` denote the dimensional formula of the permittivity of the vacuum and `[mu_(0)]` that of the permability of the vacuum.If `M="mass",L="length",T-"time"` and `I="electric current"`

Options

A. `[in_(0)]=M^(-1)L^(-3)T^(2)I`
B. `[in_(0)]=M^(-1)L^(-3)T^(4)I^(2)`
C. `[in_(0)]=MLT^(-2)I^(-2)`
D. `[in_(0)]=MLT^(-2)`

Answer

B,C

Explanation

`F=1/(4piepsilon).(q_(1)q_(2))/r^(2)`
`:.[in_(0)]=([q_(1)][q_(2)])/([F][r^(2)])=[IT]^(2)/([MLT^(-2)][L^(2)])=[M^(2)L^(-3)T^(4)I^(2)]`
Speed of light,`c=1/sqrt(in_(0)mu_(0))`
`:. [m_(0)]=1/([m_(0)][c]^(2))=1/([M^(-1)L^(-3)T^(4)I^(2)][LT^(-1)]^(2))=[MLT^(-2)I^(-2)]`