The magnitude of gravitational field intensities at distance `r_(1)` and `r_(2)` from the centre of a uniform solid sphere of radius R and mass M are `I_(1)` and `I_(2)` respectively. Find the ratio of `I_(1)//I_(2)` if (a) `r_(1) gt R` and `r_(2) gt R` and (b) `r_(1) lt R` and `r_(2) lt R` (c ) `r_(1) gt R` and `r_(2) lt R`.
Text Solution
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Gravitational field intensity for a uniform spherical distribution of mass is given by : `l=(GM)/(r^(2))` for `r gt R` and ` I =(GM)/(R^(3))r` for `r lt R`. `(a) r_(1) gt R` and `r_(2) gt R` `(l_(2))/(l_(2))=((GM//r_(1)^(2)))/((GM//r_(2)^(2)))=(r_(2)^(2))/(r_(1)^(2))` `(b) r_(1) lt R` and `r_(2) lt R` `(l_(1))/(l_(2))=((Gm//R^(3))r_(1))/((GM//R^(3))r_(2))=(r_(1))/(r_(2))` `(c ) r_(1) gt R` and `r_(2) lt R` `(l_(1))/(l_(2))=((GM//r_(1)^(2)))/((GM//R^(3))r_(2))=(R^(3))/(r_(1)^(2)r_(2))`
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