For a rigid body performing small oscillations about a fixed horizontal axis, the period of oscillations is given by. where h is the distance of the centre of mass from the axis, g is the acceleration due to gravity, and k is the radius of gyration of the body about a parallel axis through the centre of mass. Rearrange the formula to make k the subject.

Answer:

25) D

We first need to square both the LHS and RHS. We get:
T² = ⎡2π  √(k² + h²) ⎤²
       ⎣          √gh      ⎦

T² = ⎡4π² (k² + h²) ⎤
       ⎣          gh       ⎦

Move the (gh) from the RHS to the LHS.
T²gh = [4π² (k² + h²) ]

Move the (4π²) from the RHS to the LHS.
T²gh = k² + h²
4π²

Move the (h²) from the RHS to the LH
T²gh – h² = k²
 4π²

Root both the LHS and RHS
k = √(T²gh – h²)
      √(4π²)