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Moon and an apple are accelerated by the same gravitational force due to Earth. Compare the acceleration of the two. |
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Answer» Solution :The gravitational FORCE experienced by the apple due to Earth `F = - (GM_(E )M_(A))/(R^(2))` Here `M_(A)-` Mass of the apple , `M_(E ) - ` Mass of the Earth and R - Radius of the Earth Equating the above EQUATION with Newton.s 2nd law `M_(A) a_(A) = - (GM_(E)M_(A))/(R^(2))` Simplifying the above equation we get , `a_(A) = - (GM_(E))/(R^(2))` Here`a_(A)` is the acceleration of applethat is equal to.g.. Similarly the forceexperienced byMoon due toEarthis given by `F = - (GM_(E )M_(m))/(R_(m)^(2))` Here`R_(m)- ` distanceof the Monn from the `M_(m) ` - Mass of the Moon. The acceleration experienced by the Moon is givenby `a_() = - (GM_(E ))/(R_(m)^(2))` The ratiobetween the apple.s acceleration to Moon.sacceleration is given by `(a_(A))/(a_(m))=(R_(m)^(2))/(R^(2))` From Hipparchrus measurements , the distanceto the moon is 60 times thatof earth radius . `R_(m) = 60 R ` `(a_(A))/(a_(m)) = ((60R)^(2))/(R^(2)) = 3600 ` The apple.s acceleration is 3600times the acceleration of the Moon . The sameresult was obtained by Mewton using his gravitational formula . The apple.s acceleration is measuredeasily and it `9.8 "ms"^(-2)` . Moon orbitsthe Earthonce in 27.3 DAYS and by using the centripetal acceleration formula , `(a_(A))/(a_(m)) = (9.8)/((0.00272)) = 3600` which is EXACTLY what he got through his law of gravitation . |
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