The radius and mass of earth are increased by 0.5%. Which of the following statements are true at the surface of the earth

Options

A. Escape velocity will remain unchanged
B. g will increase
C. Potential energy will remain unchanged
D. g will decrease

Answer

B

Explanation

`v_(e)=sqrt((2GM)/(R ))" " therefore v_(e)prop sqrt((M)/(R ))`
and `U=-(GMm)/(R )` or `U prop (M)/(R )`
Thus if both M and R are increased by 0.5%, escape velocity and potential energy will remain unchanged.
However, `g=(GM)/(R^(2))" " therefore g prop (M)/(R^(2))`
`therefore` Thus if M and R are increased, g will decrease. Thus (a), (c ) and (d) are correct, and (b) is a wrong statement.