Mark the correct statement :.

Options

A. An electron and a proton when released from rest in uniform electric field experience the same force and the same acceleration.
B. Two equipotential surfaces may intersect.
C. A solid conducting sphere holds more charge than a hollow conducting sphere of the same radius.
D. No work is done in taking a positive charge from one point to another inside a negatively charged metallic sphere.

Explanation

To solve the question, we need to analyze the four given statements and determine which one is correct. Let's go through each option step by step.

### Step 1: Analyze Option A
**Statement:** An electron and proton when released from rest in a uniform electric field experience the same force and the same acceleration.

**Analysis:**
- The force \( F \) experienced by a charge in an electric field \( E \) is given by \( F = qE \).
- For an electron (charge \( -e \)) and a proton (charge \( +e \)), the magnitudes of the forces are equal, but they have opposite directions.
- The acceleration \( a \) is given by \( a = \frac{F}{m} \).
- Since the mass of an electron \( m_e \) is much smaller than the mass of a proton \( m_p \), the accelerations will be different.

**Conclusion:** This statement is **incorrect**.

### Step 2: Analyze Option B
**Statement:** Two equipotential surfaces may intersect.

**Analysis:**
- Equipotential surfaces are defined as surfaces where the electric potential is constant.
- If two equipotential surfaces were to intersect, it would imply that there are two different potentials at the same point in space, which is not possible.
- Therefore, equipotential surfaces cannot intersect.

**Conclusion:** This statement is **incorrect**.

### Step 3: Analyze Option C
**Statement:** A solid conducting sphere holds more charge than a hollow conducting sphere of the same radius.

**Analysis:**
- For conductors, charge resides on the surface.
- Both a solid conducting sphere and a hollow conducting sphere of the same radius can hold the same amount of charge if they are made of the same material and have the same surface area.
- The statement implies that a solid sphere can hold more charge, which is not true.

**Conclusion:** This statement is **incorrect**.

### Step 4: Analyze Option D
**Statement:** No work is done in taking a positive charge from one point to another inside a negatively charged metallic sphere.

**Analysis:**
- Inside a conductor in electrostatic equilibrium, the electric field is zero.
- Therefore, the potential is constant throughout the conductor.
- When moving a charge within this region, the work done \( W = Q(V_1 - V_2) \) is zero since \( V_1 = V_2 \).

**Conclusion:** This statement is **correct**.

### Final Answer
The correct statement is **Option D**.

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