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A : Gravitational potential is constant...

A : Gravitational potential is constant everywhere inside a spherical shell .
R : Gravitational field inside a spherical shell is zero everywhere .

A

If both Assertion & Reason are true . And the reason is the correct explanation of the assertion , then mark (1)

B

If both Assertion & Reason are true but the reason is not the correct explanation of the assertion , then mark (2)

C

If Assertion is true statement but Reason is false , then mark (3)

D

If Assertion is false statement but Reason is true , then mark (4)

Text Solution

AI Generated Solution

The correct Answer is:
To solve the given question, we need to analyze the statements A and R regarding gravitational potential and gravitational field inside a spherical shell. ### Step-by-Step Solution: 1. **Understanding the Statements**: - Statement A: "Gravitational potential is constant everywhere inside a spherical shell." - Statement R: "Gravitational field inside a spherical shell is zero everywhere." 2. **Analyzing Statement R**: - The gravitational field inside a spherical shell is indeed zero everywhere. This can be understood using the principle of superposition. - Consider a spherical shell with uniform mass distribution. The gravitational field at any point inside the shell is the vector sum of the gravitational fields due to all the mass elements of the shell. - Due to symmetry, the gravitational forces from different parts of the shell cancel each other out, resulting in a net gravitational field of zero. 3. **Analyzing Statement A**: - Gravitational potential (V) is related to the gravitational field (E) by the equation: \[ E = -\frac{dV}{dr} \] - Since we established that the gravitational field (E) inside the shell is zero, we can substitute this into the equation: \[ 0 = -\frac{dV}{dr} \] - This implies that the derivative of the gravitational potential with respect to radius is zero, meaning that V must be constant throughout the region inside the shell. 4. **Conclusion**: - Both statements A and R are true. - Statement R correctly explains Statement A, as the zero gravitational field leads to a constant gravitational potential. ### Final Answer: Both A and R are true, and R is the correct explanation of A.
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