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Chapter 6: Problem 835

let \(\mathrm{V}\) and \(\mathrm{E}\) denote the gravitational potential and gravitational field at a point. Then the match the following \(\begin{array}{ll}\text { Table }-1 & \text { Table }-2\end{array}\) (A) \(\mathrm{E}=0, \mathrm{~V}=0\) (P) At center of spherical shell (B) \(\mathrm{E} \neq 0, \mathrm{~V}=0\) (Q) At center of solid sphere (C) \(\mathrm{V} \neq 0, \mathrm{E}=0\) (R) at centre of circular ring (D) \(\mathrm{V} \neq 0, \mathrm{E} \neq 0\) (S) At centre of two point masses of equal magnitude (T) None

Short Answer

Expert verified
The correct matches are: (P) At center of spherical shell - (C) V ≠ 0, E = 0 (Q) At center of solid sphere - (C) V ≠ 0, E = 0 (R) at center of circular ring - (C) V ≠ 0, E = 0 (S) At center of two point masses of equal magnitude - (D) V ≠ 0, E ≠ 0

Step by step solution

01

Determine the scenario of V and E at the center of a spherical shell

At the center of a spherical shell, the gravitational field (E) is equal to 0, while the gravitational potential (V) is non-zero. Therefore, the correct match for the center of a spherical shell would be (C).
02

Determine the scenario of V and E at the center of a solid sphere

At the center of a solid sphere, the gravitational field (E) is equal to 0, but the gravitational potential (V) is non-zero. Consequently, the correct match for the center of a solid sphere is also (C).
03

Determine the scenario of V and E at the center of a circular ring

At the center of a circular ring, the gravitational field (E) is equal to 0, whereas the gravitational potential (V) is non-zero. Thus, the correct match for the center of a circular ring is once again (C).
04

Determine the scenario of V and E at the center of two point masses of equal magnitude

At the center of two point masses of equal magnitude, the gravitational field (E) is not equal to 0, since the field from each mass is different. The gravitational potential (V) is also non-zero. Therefore, the correct match for this case would be (D).
05

Identify matches that were not used and conclude the matching

From the above steps, we have not used (A) or (B). Additionally, we have not used (P), (Q), (R), (S), or (T). However, since (A), (B), and (C) have been thoroughly discussed in steps 1-4, we can safely conclude that the correct matches are as follows: (P) At center of spherical shell - (C) V ≠ 0, E = 0 (Q) At center of solid sphere - (C) V ≠ 0, E = 0 (R) at center of circular ring - (C) V ≠ 0, E = 0 (S) At center of two point masses of equal magnitude - (D) V ≠ 0, E ≠ 0 Thus, we've matched the appropriate scenarios of V and E with the points in Table-2.

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Most popular questions from this chapter

Radius of orbit of satellite of earth is \(\mathrm{R}\). Its \(\mathrm{KE}\) is proportional to (A) \((1 / R)\) (B) \((1 / \sqrt{\mathrm{R}})\) (C) \(\mathrm{R}\) (D) \(\left(1 / \mathrm{R}^{3 / 2}\right)\)

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