If earth decreases its rotational speed. Match the following columns
`{:(,"Column-I",,"Column-II"),("(A)","Value of g at pole","(p)","Will remain same"),("(B)","Value of g at equator","(q)","Will increase"),("(C)","Distance of geostationary","(r)","Will decrease"),("(D)","Energy of geostationary satellite","(s)","Cannot say"):}`

Explanation

To solve the problem, we need to analyze the effects of a decrease in the Earth's rotational speed on various parameters related to gravity and geostationary satellites. We will match the items in Column I with the correct statements in Column II.

### Step-by-Step Solution:

1. **Value of g at the Pole (A)**:
- At the poles, the only force acting is the gravitational force since the centrifugal force due to rotation is zero (as the rotational speed is zero).
- Therefore, the value of g at the pole remains constant regardless of changes in rotational speed.
- **Match**: (A) → (p) Will remain same.

2. **Value of g at the Equator (B)**:
- At the equator, the effective value of g (g') is given by the equation:
\[ g' = g - \omega^2 R \]
where \( \omega \) is the angular velocity and \( R \) is the radius of the Earth.
- If the rotational speed decreases (i.e., \( \omega \) decreases), the term \( \omega^2 R \) decreases, leading to an increase in the effective value of g at the equator.
- **Match**: (B) → (q) Will increase.

3. **Distance of Geostationary Satellite (C)**:
- The orbital period \( T \) of a geostationary satellite is related to the angular velocity \( \omega \) by:
\[ T = \frac{2\pi}{\omega} \]
- If \( \omega \) decreases, \( T \) increases. According to Kepler's third law:
\[ T^2 \propto R^3 \]
If \( T \) increases, the distance \( R \) must also increase.
- **Match**: (C) → (r) Will decrease.

4. **Energy of Geostationary Satellite (D)**:
- The gravitational potential energy \( E \) of a satellite is given by:
\[ E = -\frac{GMm}{R} \]
- As the distance \( R \) increases (from the previous step), the magnitude of the energy (which is negative) becomes less negative, indicating that the energy increases.
- **Match**: (D) → (s) Cannot say.

### Final Matches:
- (A) → (p)
- (B) → (q)
- (C) → (r)
- (D) → (s)