At what distance (in$$ $$metre) from the centre of the moon, the intensity of gravitational field will be zero?(Take$$, mass of earth and moon as $$5.98$$ x $$1024$$ kg and $$7.35$$ x $$1022$$ kg respectively and the distance betweenmoon and earth is $$3.855x$$ $$108$$ m.$$) [JIPMER $$2018$$]

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Given, $$Me=5.98$$×$$1024$$ kg,$$Mm=7.35$$×$$1022$$ kg  $$andr=3.855$$×$$108$$ mLet x be the distance of the point from the centre of earth, where gravitational intensity is zero. Therefore,$$GMex2=GMm3855$$×$$108-x2or$$     $$x3.855$$×$$108-x=MeMm=598$$×$$10247.35$$×$$1022$$≅$$9or$$     $$x9+x=3855$$×$$108or$$    $$x=9$$×$$3.855$$×$$108/10=3.469$$×$$108$$ mDistance from moon  $$=3.855$$×$$108-3.469$$×$$108$$                                   $$=3.86$$×$$107$$ m                                    ≅$$3.85$$×$$107$$ m

At what distance (in metre) from the centre of the moon, the intensity of gravitational field will be zero?(Take, mass of earth and moon as 5.98 x 1024 kg and 7.35 x 1022 kg respectively and the distance betweenmoon and earth is 3.855x 108 m.) [JIPMER 2018]

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