`int (dt)/(sqrt(2at - t^(2))) = a^(2) sin ^(-1)[[1)/(a) - 1]`The value of x is

Options

A. `1`
B. `-1`
C. `0`
D. `2`

Answer

c

Explanation

The quantity `(1)/(a) - 1` is dimensionless i.e.`[a] = [r]`
`:. [sqrt(2at - t^(2)] = [r]`
or, `[(dt)/(sqrt(2at -t^(2)))]= [(t)/(l)] = [M^(0) L^(0)T^(0)]`
i.e. `a^(2)` should also be dimensionless or `x= 0`