A bar magnet of magnetic moment `M_1` is suspended by a wire in a magnetic field. The tip of the wire is rotated through ` 180^(@)` , then the magnet rotated through ` 45^(@)` . Under similar conditions the magnet of magnetic moment `M_2` is rotated through ` 30^@` . Then find the ratio of `M_1 & M_2`.

Explanation

To solve the problem of finding the ratio of the magnetic moments \( M_1 \) and \( M_2 \) of two bar magnets under the given conditions, we will follow these steps:

### Step 1: Understand the Torque Equation
The torque \( \tau \) acting on a magnetic moment \( M \) in a magnetic field \( B \) is given by:
\[ \tau = M B \sin(\theta) \]
where \( \theta \) is the angle between the magnetic moment and the magnetic field.
...