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Motion In Straight Line

Question
CBSEENPH11017636

If the earth were to contract to half of its present radius without any change in mass, how would the gravitational field strength at the surface be affected?

Solution
Gravitational field strength at the surface of the earth is given by, 

                   straight E equals GM over straight R squared 
If R reduces to 1 half straight R comma then 
space straight E apostrophe equals fraction numerator GM over denominator left parenthesis straight R divided by 2 right parenthesis squared end fraction equals 4 GM over straight R squared equals 4 straight E 
Hence the strength of gravitational field increases to four times.