Assertion : If the radius of earth is decreased keeping its mass constant, effective value of g may increase or decrease at pole.
Reason : Value of g on the surface of earth is given by `g= (Gm)/(R^(2))`.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason are true but Reason is not the correct explantion of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the given question, we will analyze both the assertion and the reason step by step.

### Step 1: Understanding the Assertion
The assertion states: "If the radius of the earth is decreased keeping its mass constant, effective value of g may increase or decrease at the pole."

- If we decrease the radius of the Earth while keeping its mass constant, we need to determine how this affects the acceleration due to gravity (g) at the surface of the Earth.

### Step 2: Understanding the Formula for g
The formula for the acceleration due to gravity (g) at the surface of a spherical body like Earth is given by:
\[ g = \frac{Gm}{R^2} \]
where:
- \( G \) is the gravitational constant,
- \( m \) is the mass of the Earth,
- \( R \) is the radius of the Earth.

### Step 3: Analyzing the Effect of Decreasing Radius
If we decrease the radius \( R \) while keeping the mass \( m \) constant, we can analyze the effect on \( g \):

- Since \( g \) is inversely proportional to the square of the radius \( R \), if \( R \) decreases, \( R^2 \) also decreases.
- Therefore, \( g \) will increase because \( g \) is inversely proportional to \( R^2 \):
\[ g \propto \frac{1}{R^2} \]

### Step 4: Conclusion on the Assertion
Since decreasing the radius \( R \) (while keeping mass \( m \) constant) will always result in an increase in \( g \), the assertion that "effective value of g may increase or decrease" is **false**.

### Step 5: Understanding the Reason
The reason states: "Value of g on the surface of earth is given by \( g = \frac{Gm}{R^2} \)."

- This statement is true as it correctly describes the formula for calculating the acceleration due to gravity at the surface of the Earth.

### Final Conclusion
- The assertion is **false**.
- The reason is **true**.

Thus, the correct answer is that the assertion is false while the reason is true.