a deflection magnetometer is adjusted in the usual way.when a magnetometer is introduced,the deflection observed is @(theta),and the period of oscillation of the needle in the mangetometer is T.when the magnet is removed the period of oscillations is T0.the relation between Tand T0 is A)T^2=T0^2 Cos @

When deflection magnetometer is rest in usual way the field due to magnet (F) and horizontal component (H) of earth's field are perpendicular to each other. In this setting
T=2πIMF2+H2−−−−−−−√−−−−−−−−−−−−√...(i)T=2πIMF2+H2...(i)
After removing the magnet
T0=2πIMH−−−−−√...(ii)T0=2πIMH...(ii)
We know,FH=tanθFH=tanθ
Dividing (i) by (ii), we get,
TT0=HF−−√2+H2−−−−−−−−−−√TT0=HF2+H2
=HH2tan2θ+H2−−−−−−−−−−−−√−−−−−−−−−−−−−−−√=HHsec2θ−−−−−√−−−−−−−−√=cosθ−−−−√=HH2tan2θ+H2=HHsec2θ=cosθ
⇒T2T20=cosθ∴T2=T20cosθ