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Chapter 6: Problem 723

What is the intensity of gravitational field at the center of spherical shell (A) \(\left(\mathrm{Gm} / \mathrm{r}^{2}\right)\) (B) \(\mathrm{g}\) (C) zero (D) None of these

Short Answer

Expert verified
The intensity of the gravitational field at the center of a spherical shell is zero, as the gravitational field created by each mass element of the shell cancels out due to symmetry. Therefore, the correct answer is (C) zero.

Step by step solution

01

Find Gravitational Field Intensity Formula

We need to recall the formula for the intensity of the gravitational field, which is given by: \[g = \frac{Gm}{r^2}\] Here, \(g\) is the intensity of the gravitational field, \(G\) is the gravitational constant, \(m\) is the mass of the object, and \(r\) is the distance between the center of the mass and the point where we want to find the gravitational field intensity.
02

Apply the Principle of Superposition

Due to the uniform mass distribution and symmetry of the spherical shell, we can determine the gravitational field at its center by calculating the gravitational field created by each mass element of the shell and summing them up. By symmetry, we know that the gravitational field created by opposite mass elements will cancel each other out. This means that at the center of the spherical shell, the net gravitational field intensity will be zero.
03

Conclusion

By applying the principle of superposition and considering the symmetry of the problem, we found out that the intensity of the gravitational field at the center of a spherical shell is zero. Therefore, the correct answer is (C) zero.

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