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CBSE Class 11-science Answered

what is the % change in g on the earth's surface if the radius of earth shrinks 2% keeping mass constant?
Asked by archana | 25 Nov, 2015, 07:28: PM
answered-by-expert Expert Answer
The acceleration due to gravity at the surface of earth is given as
g = G m / R2  .
The radius of eath decreases by 2 %, therefore
begin mathsize 12px style straight g equals Gm over straight R squared The space radius space of space eath space decreases space by space 2 space percent sign comma space therefore straight R apostrophe space equals space straight R space minus space 0.02 space straight R space equals space 0.98 straight R. Now space acceleration space due space to space gravity space will space be space colon space straight g apostrophe space equals Gm over open parentheses 0.98 straight R close parentheses squared space space space equals space 1.04 space straight g space Percentage space increase space in space acceleration space due space to space gravity space is space given space as fraction numerator straight g apostrophe space minus space straight g over denominator straight g end fraction space straight x space 100 space equals space space fraction numerator 1.04 straight g space minus space straight g over denominator straight g end fraction space straight x space 100 space equals space 4 space percent sign end style
Answered by Yashvanti Jain | 25 Nov, 2015, 08:03: PM

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