Question

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of 3 s and 4 s respectively. If their moments of inertia are in the ratio of 3 : 2 then the ratio of their magnetic moments will be ______.

Options

• 2 : 1

• 8 : 3

• 1 : 3

• 27 : 16

Answer 1

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of 3 s and 4 s respectively. If their moments of inertia are in the ratio of 3 : 2 then the ratio of their magnetic moments will be 8 : 3.

Explanation:

As, T = 2π `sqrt(1/"MB")`

⇒ T₂ ∝ `1/"M"`

⇒ M ∝ `"I"/"T"^2`

⇒ `"M"_1/"M"_2=("I"_1/"I"_2)("T"_2/"T"_1)^2`

= `3/2xx(4/3)^2`

= `3/2xx16/9`

= `8/3`