Magnetic field due to currentHard

Question

A magnet makes 40 oscillation per minute at a paece having magnetic intensity of 0.1 × 10-5 tesla. At another place it takes 2.5 sec to complete one oscillation. The value of earth′s horizontal field at the place is

Options

A.0.76 × 10-6 tesla
B.0.18 × 10-6 tesla
C.0.09 × 10-6 tesla
D.0.36 × 10-6 tesla

Solution

Time period of vibration of a magnet is
T = 2×
For the same magnet, Iand M are constant wfere M = nagnetic moment,
I = moment of inertia of magnet.
T = 2×
First case
T1 = = 1.5 sec
H1 = 0.1 × 10-5T,T2 = 2.5 sec, H2 = ?
⇒    
⇒    
⇒     H2 = × 10-6
⇒     H2 = × 10-6 = 0.36 × 10-6 T

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