Gravitation Question 107
Question: A mass M is split into two parts, m and (M?m), which are then separated by a certain distance. What ratio of m/M maximizes the gravitational force between the two parts [AMU 2000]
Options:
A) 1/3
B) 1/2
C) 1/4
D) 1/5
Show Answer
Answer:
Correct Answer: B
Solution:
$ [F=\frac{Gm(M-m)}{r^{2}}] $ For maximum force $ [\frac{dF}{dm}=0] $ Þ$ [\frac{d}{dm}\left( \frac{GmM}{r^{2}}-\frac{Gm^{2}}{r^{2}} \right)=0] $ Þ$ [M-2m=0,\Rightarrow ,\frac{m}{M}=\frac{1}{2}] $
