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JEE Main & Advanced Physics Gravitation / गुरुत्वाकर्षण Question Bank Critical Thinking

  • question_answer
    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]

    A) 1/3      

    B)             1/2

    C)             1/4      

    D)             1/5

    Correct Answer: B

    Solution :

                    \[F=\frac{Gm(M-m)}{{{r}^{2}}}\] For maximum force \[\frac{dF}{dm}=0\] Þ\[\frac{d}{dm}\left( \frac{GmM}{{{r}^{2}}}-\frac{G{{m}^{2}}}{{{r}^{2}}} \right)=0\] Þ\[M-2m=0\,\Rightarrow \,\frac{m}{M}=\frac{1}{2}\]


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