Question

The gravitational field due to a mass distribution is $E=K / x^{3}$ in the $x$ - direction ( $K$ is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance $x$ is (a) $K / x$ (b) $K / 2 x$ (c) $K / x^{2}$ (d) $K / 2 x^{2}$

Name: Problem 36, Chapter 8: Genius Physics (Class 11) - For IIT-JEE and CBSE
Uploaded: 2022-02-25T10:57:52-08:00
Duration: 31 s
Channel: Hast Aggarwal
Description: The gravitational field due to a mass distribution is E=K / x^3 in the x - direction ( K is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance x is (a) K / x (b) K / 2 x (c) K / x^2 (d) K / 2 x^2

   The gravitational field due to a mass distribution is $E=K / x^{3}$ in the $x$ - direction ( $K$ is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance $x$ is
(a) $K / x$
(b) $K / 2 x$
(c) $K / x^{2}$
(d) $K / 2 x^{2}$

Genius Physics (Class 11) - For IIT-JEE and CBSE

Pradeep Kshetrapal 1st Edition

Chapter 8, Problem 36

Instant Answer

Solved by Expert Hast Aggarwal

02/25/2022

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Step 1: The gravitational field due to a mass distribution is given by $E=K / x^{3}$ in the $x$ - direction. Show more…

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The gravitational field due to a mass distribution is $E=K / x^{3}$ in the $x$ - direction ( $K$ is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance $x$ is (a) $K / x$ (b) $K / 2 x$ (c) $K / x^{2}$ (d) $K / 2 x^{2}$

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Key Concepts

Gravitational Field and Potential Relationship

The gravitational potential is directly related to the gravitational field through an integration process. Specifically, the potential is defined as the negative integral of the gravitational field over distance. This relationship illustrates how the work done by or against the gravitational force leads to a change in potential energy, establishing a fundamental connection between the two concepts.

Boundary Conditions in Potential Determination

When integrating a field to find the potential, a constant of integration appears. This constant is fixed by employing a boundary condition, such as setting the potential to zero at a reference point—often taken to be infinity. This ensures a unique and physically meaningful potential function for the problem.

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