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Q.

Two point masses, each of mass M are fixed at point A and B respectively. A third point m is
released from infinity, so that it can move along y-axis under the influence of mutual gravitational attraction on it due to point masses kept at A and B respectively as shown in the figure (i). Figure (ii) represents the potential energy of system (includes m, M at A and M at B) with position of m at y-axis. (Neglect any forces other than gravity on particle C). (Given :Gm2d=12 joule, m=6kg) Given AC=d.

Choose the correct option :

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a

point mass m will perform periodic motion

b

value of U1 must be equal to –24 joule if gravitational potential energy of two point mass system
is taken to be zero when separation between them is infinite.

c

maximum speed of particle is 24 m/s

d

maximum speed of particle is 4 m/s.

answer is A, C.

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Detailed Solution

U1=GMm(2d)=4Gm2(2d)

U1=24J

From energy conservation

0+024=12mv2+(GMmd)×2+(24)

2GMmd=12mv2

4Gm2d=12mv2v=4 ms-2

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