Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
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 increaseA) 1, 2 and 3 are correct.
B) 1 and 2 are correct.
C) 2 and 4 are correct.
D) 1 and 3 are correct.
Correct Answer: A
Solution :
\[g=\frac{GM}{{{R}^{2}}}\] \[{{v}_{e}}=\sqrt{\frac{2GM}{R}}\]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%.
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