A body of mass 2 M splits into four masses { m , M - m , m , M - m } , which are rearranged to form a square as shown in the figure. The ratio of M m for which, the gravitational potential energy of the system becomes maximum is x : 1 . The value of x is ________.

Question

A body of mass 2 M splits into four masses { m , M - m , m , M - m } , which are rearranged to form a square as shown in the figure. The ratio of M m for which, the gravitational potential energy of the system becomes maximum is x : 1 . The value of x is ________.,

MARKS App · Accepted Answer

U = G m 2 a + G ( M - m ) 2 a + 2 G m ( M - m ) a + 2 G m ( M - m ) 2 a For maxima or minima of potential energy d U d m = 0 d U d m = G a ( 2 m - 2 ( M - m ) + ( M - 2 m ) 2 + 2 ( M - 2 m ) ( 4 m - 4 m - 2 2 m ) + ( - 2 M + 2 M + 2 M ) = 0 ; 2 M = 2 2 m ; M m = 2

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