QJEEM20Ph60a6: JEE Main 2020 Physics - Class 11 JEEM20Ph60a6 Solution: On the x-axis and at a distance x from the origin, the…

Question

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On the x-axis and at a distance x from the origin, the gravitational field due a mass distribution is given by

\frac{A x}{{(x^{2} + a^{2})}^{3 / 2}}

in the x-direction. The magnitude of gravitational potential on the x-axis at a distance x, taking its value to be zero at infinity, is:

Accepted Answer

Given

E_{x} = \frac{A x}{{(x^{2} + a^{2})}^{3 / 2}}

∴

\frac{- d V}{d x} = \frac{A x}{{(x^{2} + a^{2})}^{3 / 2}}

\Rightarrow

\int_{0}^{V} d V = - \int_{\infty}^{x} \frac{A x}{{(x^{2} + a^{2})}^{3 / 2}} d x

\Rightarrow

V = \frac{A}{{(x^{2} + a^{2})}^{1 / 2}}

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