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Atoms And Molecules

Question
CBSEENSC9006244

Suppose the mass of the earth somehow increases by 10% without any change in its size. What would happen to your weight? Suppose the radius of the earth becomes twice of its present radius without any change in its mass, what will happen to your weight?

Solution

Weight  = Force of gravity
That space is comma space
space space space space space space straight W space equals space m g space equals space fraction numerator G M m over denominator straight R squared end fraction 
Clearly, when the mass M of the earth increases by 10%, our weight also increase by 10% because weight is directly proportional to mass. 
Also, weight is inversely proportional to the square of radius. Therefore, when radius R of the earth becomes twice of its present radius, our weight become 1/4  of its present value.