A satellite is revolving around earth in its equatorial plane with a period `T`. If the radius of earth suddenly shrinks to half without change in the mass. Then, the new period of revolution will be

Options

A. `8 T`
B. `2sqrt(2) T`
C. `2T`
D. `T`

Explanation

To solve the problem, we need to analyze how the period of a satellite's revolution is affected when the radius of the Earth shrinks to half while keeping its mass constant.

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- Let the original radius of the Earth be \( R \).
- The satellite is revolving around the Earth with a period \( T \).

2. **Using the Formula for the Period of a Satellite**:
- The period \( T \) of a satellite in orbit is given by the formula:
\[ T = 2\pi \sqrt{\frac{r^3}{GM}} \]
where \( r \) is the distance from the center of the Earth to the satellite, \( G \) is the gravitational constant, and \( M \) is the mass of the Earth.

3. **Effect of the Radius of the Earth Shrinking**:
- If the radius of the Earth shrinks to half, the new radius \( R' \) becomes:
\[ R' = \frac{R}{2} \]
- However, the mass \( M \) of the Earth remains unchanged.

4. **Analyzing the Orbit of the Satellite**:
- The satellite's orbit is determined by its distance from the center of the Earth. If the satellite was initially at a distance \( r \) from the center of the Earth, this distance does not change simply because the Earth's radius shrinks.
- Therefore, the distance \( r \) remains the same for the satellite.

5. **Calculating the New Period**:
- Since the formula for the period \( T \) does not depend on the radius of the Earth but rather on the distance \( r \) from the center of the Earth, we can conclude that:
\[ T' = 2\pi \sqrt{\frac{r^3}{GM}} \]
- This means the new period \( T' \) is the same as the original period \( T \).

6. **Conclusion**:
- The new period of revolution remains unchanged, so:
\[ T' = T \]

### Final Answer:
The new period of revolution will be the same as the original period \( T \).