Question

two particle of masses M and 9M separated by a distance R at a point on the line joining them the gravitational field is zero the gravitational potential at that point is​

Answer 1

Let p is the point which is located x distance from M, gravitational field is zero.

so, gravitational field due to M at P = GM/x² [ along M ] .....(1)

gravitational field due to 9M at P = 9GM/(R - x)² [ along 9M ] ......(2)

a/c to question,

net gravitational field at P = 0

so, GM/x² -[9GM/(R - x)²]= 0 [we take negative because both field are in opposite directions.]

or, GM/x² = 9GM/(R - x)²

or, 1/x = 3/(R - x)

or, R = 4x => x = R/4 and (R - x) = 3R/4

now, gravitational potential due to M at P = -GM/(R/4) = -4GM/R

gravitational potential due to 9M at P = -G(9M)/(3R/4) = -12GM/R

so, net gravitational potential at P = -4GM/R - 12GM/R = -16GM/R