The force of repulsion between two point charges is F, when these are at distance 0.5m apart. Now the point charges are replaced by spheres of radii 5 cm each having the same charge as that of the respective point charge. The distance between their centres is again kept 0.5 m. Then the force of repulsion will

Options

A. increase
B. decrease
C. remain F
D. become `(10 F)/9`

Answer

To solve the problem, we need to analyze the situation involving the two point charges and the two spheres with the same charge.

### Step-by-Step Solution:

1. **Understanding the Initial Situation**:
We have two point charges that are separated by a distance of 0.5 m, and the force of repulsion between them is given as \( F \).

2. **Coulomb's Law**:
The force of repulsion between two point charges is given by Coulomb's Law:
\[ F = k \frac{Q_1 Q_2}{r^2} \]
where \( k \) is Coulomb's constant, \( Q_1 \) and \( Q_2 \) are the magnitudes of the charges, and \( r \) is the distance between the charges.

3. **Replacing Point Charges with Spheres**:
The point charges are replaced by spheres of radius 5 cm (0.05 m) each, but the distance between their centers remains 0.5 m.

4. **Charge Distribution in Spheres**:
Since the spheres are uniformly charged, we can treat them as point charges when calculating the force between them, as long as the distance between their centers is greater than their radii.

5. **Distance Between Centers**:
The distance between the centers of the two spheres is still 0.5 m, which is the same as the distance between the point charges.

6. **Applying Coulomb's Law Again**:
Since the distance between the centers of the spheres is unchanged and the charges are the same, we can apply Coulomb's Law again:
\[ F' = k \frac{Q_1 Q_2}{(0.5)^2} \]
This shows that the force \( F' \) is still dependent on the same parameters as before.

7. **Conclusion**:
Since the distance \( r \) is the same (0.5 m), the force of repulsion \( F' \) remains equal to \( F \). Therefore, the force of repulsion will still be \( F \).

### Final Answer:
The force of repulsion will remain \( F \).