This is a good level MCQ and is very important as it helps you boost your confidence and exposes you to a different variety of questions preparing yourself more for competitive entrance examinations like NEET, JEE, etc.

So coming to the question now, this is a question from Oscillations chapter connected with Rotational Motion, Magnetism and requires some knowledge of Projectile motion too.

As we know Time period for oscillating magnet is

T=2π* root of I/MB.........(1)

where I is the moment of inertia,

M is the magnetic moment

M=x×l

x=polestrength

When the magnet is broken in two equal parts, the new magnetic dipole moment is

M′=x×l/2=M/2

I′=ML^12\2

=M/2×L^2/2

=ML^2/12*8

=I/8

New time period is

T′=2π* root of I' / M′B

Putting all the values we get

T′/T=root of 1/4= 1/2

So the final answer is 1/2.