What will be the effect on the value of the acceleration due to gravity on the earth's surface , if the radius of the earth suddenly reduces to half its present value and the mass remains constant ?

What will be the effect on the value of the acceleration due to gravit

1.	What will be the effect on the value of the acceleration due to gravity on the earth's surface , if the radius of the earth suddenly reduces to half its present value and the mass remains constant ?
Answer» Solution :LET the mass of the earth be M andits radius be R. Acceleration due to gravity on the earth.s surface, `g=(GM)/(R^2)` When the radius CHANGES to `R/2` and the mass remains `g^.=(GM)/(R/2)^2=(4GM)/(R^2)` `therefore g^. =4g` Thus, the acceleration due to gravity would be 4 TIMES the PRESENT value.