Explanation

(b) As magnets are perpendicular to each other, the resultant magnetic moment
$\ \ \ \ \ \ \ \ \ \ \ = \sqrt{M^{2} + M^{2}} = \sqrt{2}$ M
$\therefore\ \ T_{1} = 2\pi\sqrt{\frac{2I}{\sqrt{2}\ MH}}$ ….(i)
In the second case, $T_{2} = 2\pi\sqrt{\frac{I}{MH}}\ $
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{T_{2}}{T_{1}} = \frac{1}{(2)^{1/4}}$
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T_{2} = \frac{4}{(2)^{1/4}} = 3.36\ s$