Question

The radius and mass of earth are increased by 0.5%.Which of the following are true at the surface of earth? g will decrease Escape velocity will remain unchanged Potential energy will remain unchanged g will increase

• A. 1, 2 and 3 are correct.
• B. 1 and 2 are correct.
• C. 2 and 4 are correct.
• D. 1 and 3 are correct.

Answer 1

Answer: (A)

$ g=\frac{GM}{{{R}^{2}}} $ $ {{v}_{e}}=\sqrt{\frac{2GM}{R}} $ and $ u=-\frac{G{{M}_{m}}}{R} $
$ \therefore $ $ 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 Vg and 7 remains unchanged whereas g decrease by 0.5%.