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find gravitational field inside a ring of radius r at adistance x from the centre in the plane of ring

find gravitational field inside a ring of radius r at adistance x from the centre in the plane of ring

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1 Answers

ankitesh gupta
63 Points
9 years ago

 

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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