The masses of two planets are m and 16M resp. Their radii are a and 2a resp. and the centres are 10a apart. . A body of mass m is fired straight from the surface of the larger planet towards the smaller planet. What should be the minimum projectile speed so that it reaches the surface of the smaller plenet ? Obtain the exp. in G , M and a

dear student

consider the diagram 

all distances are shown



gravitational potential energy is given by 

PE=Gm1m2r(note ; all symbols have usual meaanings)total energy of m at surface of larger planet=total energy of m when it just reaches smaller planet12mv2+Gm16M2a+GmM8a=GmMa+16GmM9a12mv2=GMma(1-8+169-18)v=10.19GMa
regards

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