Explanation

(b) The time period of vibration magnetometer is given by
$T = 2\pi\sqrt{\frac{I}{MB_{H}}}$
Where I is moment of inertia, M the magnetic moment and $B_{H}$ the horizontal component of earth’s magnetic field.
Also, $I = mr^{2}$
Where m is mass and r the radius.
When mass is increased four times
$I^{'} = 4I$
$\therefore T^{'} = 2\pi\sqrt{\frac{4I}{MB_{H}}}\ $ T
$\ \ \ \ \ \ \ \ \ \ = 2 \times 2\pi\ \sqrt{\frac{I}{MB_{H}}} = 2T$