Gravitation Question 225
Question: In a cosmic event, suppose a planet heavier than the earth with mass KM (K > 1) and radius K’R (K > 1) passes through a path near the earth (M and R are the mass and radius of earth). At what closest distance from surface of planet, we are in danger ofbeing thrown into space:
Options:
A)$ [{{\left[ \frac{2KGM}{g} \right]}^{1/2}}-\frac{1}{2}K’R] $
B)$ [{{\left[ \frac{KGM}{2g} \right]}^{1/2}}-\frac{1}{2}K’R] $
C)$ [{{\left[ \frac{KGM}{g} \right]}^{1/2}}-\frac{1}{2}K’R] $
D)$ [{{\left[ \frac{KGM}{g} \right]}^{1/2}}-K’R] $
Show Answer
Answer:
Correct Answer: D
Solution:
- we will be thrown into space, if weight mg is equal to gravitational force duet to the planet. If y is the closest distance. $ [\frac{GMm}{R^{2}}=mg=\frac{G(KM)m}{{{(K’R+y)}^{2}}}] $ $ [{{(K’R+y)}^{2}}=\frac{KGM}{g}] $ $ [y={{\left( \frac{KGM}{g} \right)}^{1/2}}-K’R] $
