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28/12/2021 2:53 pm
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A particle of mass 2 M is divided into four particles of mass m, m, M - m and M - m. All particle is arranged on the vertex of the square of side a. Find the ratio of M/m, for which potential energy of this system is
(a) 2
(b) \(\frac{1}{2}\)
(c) 3
(d) \(\frac{1}{3}\)
1 Answer
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28/12/2021 2:58 pm
Correct answer: (a) 2
Explanation:
u = \(\frac{Gm^2}{a}\) + \(\frac{G(M -m)^2}{a}\) + \(\frac{2Gm(M-m_0)}{a}\) + \(\frac{2G(M-m)}{\sqrt 2a}\)
\(\frac{dU}{dm}\) = (\(\frac{G}{a}\))(2m - 2(M - m) + (M - 2m)2 + √2(M - 2m)
(4m - 4m - 2 √2m) + (-2M + 2M + √2 M) = 0; √2 M = 2 √2 m; M/m = 2
This post was modified 3 years ago by Reyana09