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Sir,The gravitational due to a uniform disc at a point in its axis is 2GMr/R²((1/r)-(1/√(r²+R²))).Andthe potential at a point in the axis is -2GM/R²(√(R²+r²)-r) where R-radius and r-distance in the axis. Also,We know that on differentiating gravitational potential we get the gravitational field at that point.But that is not the case for disc.On integrating the potential we are not getting the value of the field.Why is it so? Please help
Asked by das.atom1966 | 16 May, 2022, 05:34: PM
Your expression for gravitational force per unit mass due uniform disc is given as

.................................(1)

where G is universal gravitational constant, M is mass of disc , R is radius of disk and
r is ditance from centre of disc to the point where we are finding gravitational force

Above expression is simplified as

..................................(2)

Potential at poit r ,

By above integration we get

..................................(3)
If you want to get Force F(r) from potential , then F(r) = -dV/dr

Hence we get gravitational force by differentiating eqn.(3)

Answered by Thiyagarajan K | 16 May, 2022, 09:34: PM
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