(a) In the formula `X=3YZ^(2)`, `X` and `Z` have dimensions of capcitnce and magnetic inlduction, respectively. What are the dimensions of `Y` in `MKSQ` system?
(b) `A` qunatity `X` is given by `epsilon_(0)` `L` `((Delta)V)/((Delta)r)`, where `epsilon_(0)` is the permittivity of free space, `L` is a lenght, `DeltaV` is a potential difference and `Deltat` is a time interval. Find the dimensions of `X`.
(c) If `E,M,J` and `G` denote energy , mass , angular momentum and gravitational constant, respectively. find dimensons of `(E J^(2))/(M^(5) G^(2))`
(d) If `e,h,c` and `epsilon_(0)` are electronic charge, Planck 's constant speed of light and permittivity of free space. Find the dimensions of `(e^(2))/(2epsilon_(0)hc)`.

Options

A. `[M^(-3)L^(-1)T^(3)Q^(4)]`
B. `[M^(-3)L^(-2)T^(4)Q^(4)]`
C. `[M^(-2)L^(-2)T^(4)Q^(4)]`
D. `[M^(-3)L^(-2)T^(4)Q]`

Answer

B