Gravitation

JEE Main level, single correct, medium

36 of 223

Question 36 of 223

Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If 8R\sqrt{8}R is the distance between the centres of a ring (of mass mm) and a sphere (mass MM) where both have equal radius RR

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Answer: (D) 827GmMR2\dfrac{\sqrt{8}}{27}\dfrac{GmM}{{R}^{2}}

Gravitational field of ring
=−Gmx(R2+x2)3/2=-\dfrac{Gmx}{{\left({R}^{2}+{x}^{2}\right)}^{3/2}}
Force between sphere & ring
=GmM(8R)(R2+8R2)3/2=\dfrac{GmM\left(\sqrt{8}R\right)}{{\left({R}^{2}+8{R}^{2}\right)}^{3/2}}
=GmMR2×827=\dfrac{GmM}{{R}^{2}}\times \dfrac{\sqrt{8}}{27}

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