A positively charged disc is placed on a horizontal plane. A charged particle is released from a certain height on its axis. The particle just reaches the centre of the disc. Select the correct alternative.

Options

A. particle has negative charge on it
B. total potential energy (gravitationl+electrostatic) of the particle first increases, then decreases
C. total potential energy of the particle first decreases, then increases
D. total potential energy of the particle contilnously decreses

Explanation

To solve the problem step by step, let's analyze the situation involving a positively charged disc and a charged particle released from a height along the axis of the disc.

### Step 1: Understand the Initial Conditions
- The charged particle is released from a certain height above the disc, which means it starts with an initial potential energy due to its height and electric potential energy due to the electric field created by the positively charged disc.
- The initial velocity of the particle is zero (it is released from rest).

**Hint:** Consider the forces acting on the charged particle when it is released.

### Step 2: Analyze Forces Acting on the Particle
- The particle experiences two forces: gravitational force (downward) and electric force (due to the positively charged disc).
- If the particle is negatively charged, it will be attracted towards the positively charged disc.

**Hint:** Think about how the direction of the electric force affects the motion of the particle.

### Step 3: Apply Conservation of Energy
- Since there are no non-conservative forces acting on the system, we can apply the principle of conservation of mechanical energy.
- The total mechanical energy at the initial point (A) must equal the total mechanical energy at the final point (C).

**Hint:** Write down the equation for conservation of energy: \( KE_A + PE_A = KE_C + PE_C \).

### Step 4: Evaluate Energy at Points A and C
- At point A (initial position), the kinetic energy (KE_A) is zero because the particle is at rest. The potential energy (PE_A) consists of gravitational potential energy and electric potential energy.
- At point C (the center of the disc), the kinetic energy (KE_C) is also zero, as the problem states that the particle just reaches the center and stops there. Therefore, the potential energy at point C (PE_C) must equal the potential energy at point A (PE_A).

**Hint:** Remember that potential energy is related to the height and the electric field.

### Step 5: Analyze the Motion Between Points A and C
- As the particle moves from A to C, it will accelerate due to the net force acting on it (the sum of gravitational and electric forces).
- There will be a point (let's call it B) where the particle has maximum velocity and thus maximum kinetic energy.

**Hint:** Consider how the potential energy changes as the particle moves from A to C.

### Step 6: Determine the Behavior of Potential Energy
- As the particle descends from A to C, the potential energy decreases until it reaches point B (where kinetic energy is maximum).
- After point B, as the particle approaches point C, the potential energy increases back to the value at point A.

**Hint:** Visualize the energy transformation: potential energy decreases, reaches a minimum, and then increases.

### Step 7: Conclude the Correct Option
- The correct alternative states that the total potential energy of the particle first decreases and then increases as it moves from point A to point C.
- Therefore, the correct answer is option C.

**Final Answer:** The correct alternative is C: The total potential energy of the particle first decreases and then increases.