If equation `int (dt)/(sqrt(3a - 2t^(2))) = a^(x) sin ^(-1) ((r^(2))/(a^(2)) - 1)`, the value of x is

Options

A. `(3)/(2) `
B. `0`
C. `(1)/(2)`
D. `-(1)/(2)`

Answer

b

Explanation

`((t^(2))/(a^(2)) - 1)` is dimensionless
` :. [a] = [t]`
As, `sqrt((3at - 2t^(2))) = [r]`
`:. [(dt)/sqrt((3at - t^(2)))] = ([t])/([t])=[M^(0)L^(0)T^(0)]`
`a^(2)` should be dimensionless so `x =0`