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Atoms And Molecules

Question
CBSEENSC9006146

A body weighs 63 N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?

Solution

Given comma space

Weight space of space the space body comma space mg space space equals space 63 space straight N

Height space is space equal space to space half space the space radius space of space the space earth.
straight i. straight e. comma space space straight h space equals space straight R over 2
Now comma space
straight g subscript straight h space equals space straight g open parentheses fraction numerator straight R over denominator straight R plus straight h end fraction close parentheses squared space
space space space space space equals space straight g open parentheses fraction numerator straight R over denominator straight R plus begin display style straight R over 2 end style end fraction close parentheses squared space
space space space space equals space straight g open parentheses 2 over 3 close parentheses squared space
space space space space equals space 4 over 9 straight g
therefore  Gravitational force at height equal to half the radius of the earth. 
W space equals space mg subscript straight h space
space space space space equals space 4 over 9 mg space
space space space space equals space 4 over 9 cross times 63 space straight N space
space space space space equals space 28 space straight N.