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Motion In Straight Line

Question
CBSEENPH11017817

A body weighs 64 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

Weight of the body = mg = 64 N
So, mass of the body, m = 64 / g = 64/ 10 = 6.4 kg
At height h, the value of g' is given by, 
straight g apostrophe space equals space straight g space straight R squared over open parentheses straight R plus straight h close parentheses squared space equals space 10 open parentheses space fraction numerator straight R over denominator straight R space plus space straight R divided by 2 end fraction close parentheses squared space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 10 space straight x space 4 divided by 9

therefore space Weight space at space straight a space height space straight h space equals space mg apostrophe space

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 6.4 space straight x space 10 space straight x space 4 divided by 9 space straight N

space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals 28.44 space straight N