Consider metal ring kept on a horizontal plane . A bar magnet is held above the ring with its length along the axis is held above the ring with its length along the axis of the ring . If the magnet is dropped freely the acceleration of the falling magnet is : ( g is accelration due to gravity )

Options

A. (a)More than g
B. (b)Equal to g
C. (c)Less than g
D. (d)Depends on mass of magnet

Answer

To solve the problem of determining the acceleration of a falling magnet above a metal ring, we can follow these steps:

### Step 1: Understand the Setup
We have a metal ring placed on a horizontal plane and a bar magnet held above it. The magnet is oriented such that its length is along the axis of the ring.

**Hint:** Visualize the setup to understand how the magnet and the ring interact.

### Step 2: Consider the Forces Acting on the Magnet
When the magnet is dropped, it experiences two main forces:
1. The gravitational force acting downward (mg, where m is the mass of the magnet and g is the acceleration due to gravity).
2. An induced magnetic force due to the change in magnetic flux through the ring as the magnet falls.

**Hint:** Remember that the gravitational force is constant, but the induced force will depend on the motion of the magnet.

### Step 3: Analyze the Induced EMF
As the magnet falls, it changes the magnetic flux linked with the metal ring. According to Faraday's law of electromagnetic induction, a change in magnetic flux induces an electromotive force (EMF) in the ring. This induced EMF creates a current in the ring, which in turn generates a magnetic field that opposes the motion of the falling magnet (Lenz's Law).

**Hint:** Recall that Lenz's Law states that the direction of induced current will always oppose the change in magnetic flux.

### Step 4: Determine the Effect on Acceleration
The induced magnetic force acts upward against the gravitational force. Therefore, the net force acting on the magnet will be less than the gravitational force. This results in a net downward acceleration that is less than g.

**Hint:** Use Newton's second law (F = ma) to relate the net force to the acceleration of the magnet.

### Step 5: Conclusion
Since the upward induced force opposes the downward gravitational force, the acceleration of the falling magnet will be less than g. Hence, we conclude that the acceleration of the falling magnet is less than the acceleration due to gravity.

**Final Answer:** The acceleration of the falling magnet is less than g.

### Summary of Steps:
1. Visualize the setup with the magnet and the ring.
2. Identify the forces acting on the magnet.
3. Analyze the induced EMF and its effects.
4. Conclude that the net force results in an acceleration less than g.