A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is `10V`. The potential at the distance `3 cm` from the centre of the sphere is:

Options

A. zero
B. 10 V
C. same as at a point 5 cm away from the surface
D. same as at a point 25 cm away from the surface

Answer

To solve the problem, we need to determine the potential at a distance of 3 cm from the center of a hollow metal sphere with a radius of 5 cm, given that the potential on its surface is 10 V.

### Step-by-Step Solution:

1. **Understand the Properties of a Hollow Metal Sphere:**
- A hollow metal sphere behaves as a conductor. Inside a conductor, the electric field is zero. This means that the potential inside the hollow sphere is constant and equal to the potential on its surface.

2. **Identify the Given Values:**
- Radius of the hollow metal sphere, \( R = 5 \, \text{cm} \)
- Potential on the surface of the sphere, \( V_{\text{surface}} = 10 \, \text{V} \)
- Distance from the center where we need to find the potential, \( r = 3 \, \text{cm} \)

3. **Determine the Location of the Point of Interest:**
- Since the distance \( r = 3 \, \text{cm} \) is less than the radius \( R = 5 \, \text{cm} \), this point lies inside the hollow metal sphere.

4. **Apply the Concept of Constant Potential:**
- Because the electric field inside the hollow metal sphere is zero, the potential remains constant throughout the interior of the sphere. Therefore, the potential at any point inside the sphere is equal to the potential at its surface.

5. **Conclude the Potential Inside the Sphere:**
- Since the potential on the surface is 10 V, the potential at a distance of 3 cm from the center (which is inside the sphere) is also:
\[ V = V_{\text{surface}} = 10 \, \text{V} \]

### Final Answer:
The potential at the distance of 3 cm from the center of the sphere is **10 V**.

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