M for spherical masses grav gm, m f 2 this formula is conditional & only used when density of object is uniform of function of raciat distance. if object has ot

M For Spherical Masses grav GM, M F 2 This formula is conditional & only used when density of object is uniform of function of raciat distance. If object has other shapes or density Is nof unform then integration is used for force calculatie particle of mass m then force between these particles is not given by above formula M Example: As shown in figure if one of the object is block of mass M and another is a point GMm 1.e. F d because density is not uniform To solve this we have to use integration as follows First take a mass element dM at distance x from one side of rod and length of element is dx (Here length of rod is ) U2- dM X= 0 m (d x + 02) Force due to element taken Gm dM dF (d-x+tl2) Gm dM F-ld-x+l/2) We have to convert dM in terms of dx l length has mass M M unitary method (use only for uniform object) dx length has mass dx Substituting M dM-dx Therefore, Gravitational force between both particles is Gm(M/)dx F Jo (d-x+/2 1 GmM F L(d-x + l/2) J, (-1) -1 GmM GmM F: d-(/2) d-214 GmM F- df-2/4