Gravitation Question 110
Question: The radius and mass of earth are increased by 0.5%. Which of the following statements are true at the surface of the earth[Roorkee 2000]
Options:
A) g will increase
B) g will decrease
C) Escape velocity will remain unchanged
D) Potential energy will remain unchanged
Show Answer
Answer:
Correct Answer: B
Solution:
$ [g=\frac{GM}{R^{2}},v_{e}=\sqrt{\frac{2GM}{R}}] $ and $ [U=\frac{-GMm}{R}] $ \ $ [g\propto \frac{M}{R^{2}},v_{e}\propto \sqrt{\frac{M}{R}}] $ and $ [U\propto \frac{M}{R}] $ If both mass and radius are increased by 0.5% then $ [v_{e}] $ and U remains unchanged where as g decrease by 0.5%.
