Explain how to solve this :

Dear Student,
The time constant of oscillation is given by:
$T_1=2\pi \sqrt{\frac{m}{k}}$
When the spring is cut into two equal halves. The spring constant of each half becomes 2k.
The new time constant of oscillation of half spring  is given by:
$T_2=2\pi \sqrt{\frac{m}{2k}}$
So, the ratio
$\frac{T_2}{T_1}=\sqrt{\frac{1}{2}}=\frac{1}{\sqrt{2}}$
Ans (B)
Regards