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(C) The gravitational potential energy $U$ of a system of point masses is the sum of the potential energies of all pairs of masses.For three masses $m

Vedclass · Accepted Answer

$-11 \frac{Gm^2}{a}$

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(C) The gravitational potential energy $U$ of a system of point masses is the sum of the potential energies of all pairs of masses.For three masses $m_1, m_2, m_3$ at distances $r_{12}, r_{23}, r_{31}$,the total potential energy is $U = -G \left( \frac{m_1 m_2}{r_{12}} + \frac{m_2 m_3}{r_{23}} + \frac{m_3 m_1}{r_{31}} \right)$.Here,$m_1 = m$,$m_2 = 2m$,$m_3 = 3m$,and $r_{12} = r_{23} = r_{31} = a$.Substituting these values:$U = -\frac{G}{a} [ (m)(2m) + (2m)(3m) + (3m)(m) ]$$U = -\frac{G}{a} [ 2m^2 + 6m^2 + 3m^2 ]$$U = -\frac{G}{a} [ 11m^2 ]$$U = -11 \frac{Gm^2}{a}$.

The gravitational potential energy of a system of three masses $m$,$2m$,and $3m$ placed at the three vertices of an equilateral triangle of side '$a$' is:

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