Q. 94.0( 1 Vote )

Derive an expression for the gravitational field due to a uniform rod of length L and mass M at a point on its perpendicular bisector at a distance d from the center.

Answer :

Here, the mass of the rod is and the length is .

Let us take an element of length dx at a distance x from the center of the rod.


Mass of the element is


The element is at a distance d from the rod.


The horizontal components cancel out and the field is in the negative y direction given by


—————(1)


We know,


—————(2)



Substituting (2) in (1)



Which gives us



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