Question

32:The gravitational potential energy of system of
three point masses each of mass 2 kg placed at
the three vertices of an equilateral triangle of side
10 cm is
(1)--60 G
(2) - 120 G
(3) - 90 G
(4) -- 100 G​

Answer 1

Answer:

Gravitaional potential energy of system of three point masses placed at three vertices of equilateral triangle would be -120G .Hence option (2) is correct

Explanation:

The graviational potential energy between a pair of masses is given as

   $U= \frac{GMm}{r}$

where M and m are mass of two objects

Here we are given system of three point masses each of 2kg .

so total potential energy of system would be

$U = -(U _{12} + U_{23} + U_{13} )\\\\U = -(\frac{Gm^{2} }{L} + \frac{Gm^{2} }{L} + \frac{Gm^{2} }{L})\\ \\U=- (3\times \frac{Gm^{2} }{L})\\\\U= -(3\times \frac{G\times 2^{2}}{L})\\\\U= - 120 G$

So correct answer should be -120 G .