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Find the point at which the gravitational force acting on any mass is zero due to the earth and the moon system. (such a point is called neutral point). The mass of the moon and the distance between the earth and the moon is 3,85,000 km.

Answer» <html><body><p></p>Solution :<img src="https://doubtnut-static.s.llnwi.net/static/physics_images/AKS_DOC_OBJ_PHY_XI_V01_B_C09_SLV_013_S01.png" width="80%"/> <br/> Let `m_(1)` and `m_(2)` be the masses of the <a href="https://interviewquestions.tuteehub.com/tag/earth-13129" style="font-weight:bold;" target="_blank" title="Click to know more about EARTH">EARTH</a> and the moon separated by a distance d. <br/> Consider an object of mass m at a point P, which is at a distance X from `m_(1)`. The force due to mass `m_(1)` on the mass m is `F_(1) = (<a href="https://interviewquestions.tuteehub.com/tag/gm-1008640" style="font-weight:bold;" target="_blank" title="Click to know more about GM">GM</a> m_(1))/(X^(2))` <a href="https://interviewquestions.tuteehub.com/tag/towards-7269729" style="font-weight:bold;" target="_blank" title="Click to know more about TOWARDS">TOWARDS</a> `m_(1)` and <br/> The force due to mass `m_(2)` on the mass m is <br/> `F_(2) = (Gm m_(2))/((d-x)^(2))` towards `m_(2)` <br/> If the <a href="https://interviewquestions.tuteehub.com/tag/resultant-1187362" style="font-weight:bold;" target="_blank" title="Click to know more about RESULTANT">RESULTANT</a> force on the mass .m. is to be zero, `F_(1)` must be equal to `F_(2)` in magnitude and they are oppositely <a href="https://interviewquestions.tuteehub.com/tag/directe-7360898" style="font-weight:bold;" target="_blank" title="Click to know more about DIRECTE">DIRECTE</a> `(Gm m_(1))/(x^(2)) = (Gm m_(2))/((d-x)^(2)) rarr x = 38,500 km` <br/> from moon here `m_(1) = M` mass of the moon, `m_(2) = 81M`, mass of the earth</body></html>


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