Question

For a particle inside a uniform spherical shell, the gravitational force on the particle is:

• A. Infinite
• B. Zero
• C. \( \frac{-G m_1 m_2}{r^2} \)
• D. \( \frac{G m_1 m_2}{r^2} \)

Hint:

Inside a uniform spherical shell, a particle experiences no net gravitational force because of the symmetrical distribution of mass.

Answer 1

The Correct Option is B

Step 1: {Apply shell theorem} 
The shell theorem states that a uniform spherical shell of mass exerts zero net gravitational force on a particle inside it. 
Step 2: {Explain force cancellation} 
Forces from opposite sides of the shell cancel out due to symmetry, leaving: Net gravitational force = 0.
Thus, the correct answer is zero. 
 

Answer 2

Step 1: According to Newton's Shell Theorem:
- A uniform spherical shell of mass exerts no net gravitational force on a particle located anywhere inside it.

Step 2: The gravitational attraction from all the mass elements of the shell cancels out symmetrically when the particle is inside the shell.
Even if the particle is not at the center, the vector sum of gravitational forces from all sides of the shell adds up to zero.

Step 3: Mathematically, the result from Newton’s Shell Theorem for a point inside a spherical shell is:
\( F = 0 \)

Final Answer: Zero