A deflection magnetometer is adjusted and a magnet moment M is placed on it in the usual manner and the observed deflection is $\theta$. The period of oscillation of the needed before setting to the deflection is $T$. When the magnet is removed, the period of oscillation of needle is $T_0$ before settling to $0^{\circ}-0^{\circ}$. If the earth's induced magnetic field is $B_{H},$ the relation between $T$ and $T_0$ is

Question

$$(a)\;T^2-T^2_0 \cos \theta \quad (b)\;T^2=\frac{T^2_0}{\cos \theta} \quad (c)\;T=T_0 \cos \theta \quad (d)\;T=\frac{T_0}{\cos \theta}$$