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Assertion : One two sides of a point mas...

Assertion : One two sides of a point mass, gravitational field strength is same at same distance,
Reason : As we move away from a point mass, value of gravitational potential decreases.

A

If both Assertin and Reason are correct and Reason is the correct explanation of Assertion

B

If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion

C

If Assertion is true but Reason is false

D

If Assertion is false but Reason is true

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AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze both the assertion and the reason provided in the question. ### Step 1: Analyze the Assertion The assertion states that the gravitational field strength is the same on two sides of a point mass at the same distance. - **Gravitational Field Strength Formula**: The gravitational field strength (E) due to a point mass (m) at a distance (r) is given by: \[ E = \frac{Gm}{r^2} \] where G is the gravitational constant. - **Distance Consideration**: If we have two points A and B, both at the same distance (r) from the point mass, we can calculate the gravitational field strength at both points. Since the mass (m) and distance (r) are the same for both points, the magnitudes of the gravitational field strength (E_A and E_B) will be equal: \[ E_A = E_B \] - **Direction of the Gravitational Field**: However, gravitational field strength is a vector quantity. The direction of the gravitational field at point A will be towards the mass, and at point B, it will also be towards the mass but in the opposite direction. Therefore, while the magnitudes are the same, the vectors are not: \[ \text{Direction of } E_A \neq \text{Direction of } E_B \] - **Conclusion on Assertion**: The assertion is false because it does not take into account the direction of the gravitational field vectors. ### Step 2: Analyze the Reason The reason states that as we move away from a point mass, the value of gravitational potential decreases. - **Gravitational Potential Formula**: The gravitational potential (V) at a distance (r) from a point mass (m) is given by: \[ V = -\frac{Gm}{r} \] - **Behavior of Gravitational Potential**: As the distance (r) increases, the magnitude of the gravitational potential (ignoring the negative sign) decreases because it is inversely proportional to r: \[ V \propto -\frac{1}{r} \] - **Conclusion on Reason**: The reason is true because as we move further away from the mass, the gravitational potential indeed decreases in magnitude. ### Final Conclusion Based on the analysis: - The assertion is false. - The reason is true. Thus, the correct answer is that the assertion is false, and the reason is true.

To solve the problem, we need to analyze both the assertion and the reason provided in the question. ### Step 1: Analyze the Assertion The assertion states that the gravitational field strength is the same on two sides of a point mass at the same distance. - **Gravitational Field Strength Formula**: The gravitational field strength (E) due to a point mass (m) at a distance (r) is given by: \[ E = \frac{Gm}{r^2} ...
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