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  • Two bodies of mass m and 9m are placed at a distance R. The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be (G = gravitational constant) :<

Two bodies of mass m and 9m are placed at a distance R. The gravitational potential on the line joining the bodies where the gravitational field equals zero, will be (G = gravitational constant) :

Option: 1

-\frac{8 \mathrm{Gm}}{\mathrm{R}}


Option: 2

-\frac{12 \mathrm{Gm}}{\mathrm{R}}


Option: 3

-\frac{16 \mathrm{Gm}}{\mathrm{R}}


Option: 4

-\frac{20 \mathrm{Gm}}{\mathrm{R}}


Answers (1)

best_answer

Let point P is the point where the gravitational field equals zero

\begin{aligned} & r_1=\left(\frac{\sqrt{m}}{\sqrt{9 m}+\sqrt{m}}\right) R=\frac{R}{4} \\ & r_2=\frac{3 R}{4} \\ & V=-\frac{G m}{\left(\frac{R}{4}\right)}-\frac{G(9 m)}{\left(\frac{3 R}{4}\right)} \\ & V=-\frac{16 \mathrm{Gm}}{R} \end{aligned}

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sudhir.kumar

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