A magnet is suspended horizontally in the earth's magnetic field. When it is displaced and then released, it oscillates in a horizontal plane with a period T. If a piece of wood of the same moment of inertia (about the axis of rotation) as the magnet is attached to the magnet, what would the new period of oscillation of the system?

Question

A magnet is suspended horizontally in the earth's magnetic field. When it is displaced and then released, it oscillates in a horizontal plane with a period T. If a piece of wood of the same moment of inertia (about the axis of rotation) as the magnet is attached to the magnet, what would the new period of oscillation of the system? (A) (T/3) (B) (T/2) (C) (T/√2) (D) T √2

Tardigrade Admin · Accepted Answer

Due to wood moment of inertia of the system becomes twice but there is no change in magnetic moment of the system. Hence, T=2 π √(I/M BH) ⇒ T propto √I ⇒ T'=√2 T

$\frac{T}{3}$

$\frac{T}{2}$

$\frac{T}{2}$

$T 2$

Due to wood moment of inertia of the system becomes twice but there is no change in magnetic moment of the system.
Hence,
$T = 2 π \frac{I}{M B _{H}}$
$\Rightarrow T \propto I$
$\Rightarrow T^{'} = 2 T$

3T​

2T​

2​T​

T2​

Due to wood moment of inertia of the system becomes twice but there is no change in magnetic moment of the system. Hence, T=2πMBH​I​​ ⇒T∝I​ ⇒T′=2​T

$\frac{T}{3}$

$\frac{T}{2}$

$\frac{T}{2}$

$T 2$

Due to wood moment of inertia of the system becomes twice but there is no change in magnetic moment of the system.
Hence,
$T = 2 π \frac{I}{M B _{H}}$
$\Rightarrow T \propto I$
$\Rightarrow T^{'} = 2 T$