A magnetic needle is oscillating in earth’s horizontal field $\left({\mathrm{B}}_{\mathrm{H}}\right)$ with a time period of 0.5 sec. A dip needle of same magnetic dipole moment, mass and geometry oscillator in earth’s vertical field $\left({\mathrm{B}}_{\mathrm{V}}\right)$with a time period of 1 sec. Then angle of dip at that place is

• A

  ${\tan }^{-1}\left(\frac{1}{2}\right)$

• B

  ${\tan }^{-1}\left(2\right)$

• C

  ${\tan }^{-1}\left(\frac{1}{8}\right)$

• D

  ${\tan }^{-1}\left(\frac{1}{4}\right)$