Torque

The torque is given by the formula: where: - is the applied force, - is the distance from the axis of rotation (since ), - is the angle between the force and the horizontal axis (because the force is in the plane of the wheel and the angle given is with respect to the horizontal axis).
Now, substitute the values into the torque formula: Using , we get: Thus, the torque is .

The torque ( ) acting on a bar magnet placed in a uniform magnetic field is given by the equation: Where: - is the magnetic moment of the bar magnet, - is the magnetic field strength, - is the angle between the magnetic moment and the magnetic field. When the bar magnet is perpendicular to the magnetic field, , and the torque is maximum, given by: If the couple acting on the magnet is to be halved, the new torque must be half of the maximum torque. Therefore, we require: Solving for , we get:
Thus, Therefore, the angle by which the bar magnet must be rotated to halve the torque is , and the correct answer is B.