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Three identical stars, each of mass M, form an equilateral triangle (stars are positioned at the corners) that rotates around the centre of the triangle. The system is isolated and edge length of triangle is ‘L’. The minimum amount of work done that is required to dismantle the system is (Assume L is much greater than size of stars)

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a

GM22L

b

3GM22L

c

3GM24L

d

3GM2L

answer is B.

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Detailed Solution

Given mass of each star= MLength of triangle =LTotal energy of system initially =KE+PE PE=−3GM2LKE=312MV2 Where MV2R=2GM2L2cos300=3GM2L2& R=L3∴KE=312MV2=32×GM2LHence, TEi=−3GM2L+3GM22L=−32GM2L TEf=0 Work done = TEf−TEi=32GM2L

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Three identical stars, each of mass M, form an equilateral triangle (stars are positioned at the corners) that rotates around the centre of the triangle. The system is isolated and edge length of triangle is ‘L’. The minimum amount of work done that is required to dismantle the system is (Assume L is much greater than size of stars)