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find gravitational field inside a ring of radius r at adistance x from the centre in the plane of ring
dEG IS GRAVITATIONAL FIELD ASSUME A SMALL ELEMENT OF MASS ''dM'' ON THE RING GRAVITATIONAL FIELD DUE TO THE OBJECT ON THE SMALL ELEMENT IS dEG BREAK THEM INTO COMPONENTS dEGCOS@ , AND dEG SIN@
SINCE THERE IS SYMMETRY OF THE HORIZONTAL COMPONENT (dEGSIN@) ON BOTH THE SIDES OF THE OBJECT SO HORIZONTAL COMPONENT WILL GET CANCELLED SO YOU ANSWER WILL BE dEGCOS@
dEG=G(dM)/(DISTANCE)2 NOW THE DISTANCE IS (R2+X2)1/2 LET IT BE D NOW dEGCOS@= G(dM)COS@/D2
INTEGRATE THIS FUNCTION YOU GET EG=GMCOS@/D2 SINCE INTEGRATION IS SUMMATION THEREFORE INTEGRATION OF dM WILL BE THE TOTAL MASS M
FROM THE DIAGRAM USING PHYTHOGORUS THEORM COS@=X/D
SUBSTITUTING YOU GET EG=GMX/D3
OR EG = GMX/(X2+R2)3/2 PLZZZZZ approve if it helped you
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