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  • Two hypothetical planents of masses m and 2m are at rest when they are infinite distance apart. Because of the gravitation force they move towards each other along the line joining their centres. W

Two hypothetical planents of masses m and 2m are at rest when they are infinite distance apart. Because of the gravitation force they move towards each other along the line joining their centres. What is their speed when their sepration is d? (Speed of m is v1 and that of 2m is v2)?

 

Option: 1

v_1=v_2


Option: 2

v_1=2m\sqrt{\frac{2G}{d(3m)}}, v_2=m\sqrt{\frac{2G}{d(3m)}}


Option: 3

v_1=m\sqrt{\frac{2G}{d(3m)}},v_2=2m\sqrt{\frac{2G}{d(3m)}}


Option: 4

v_1=2m\sqrt{\frac{2G}{m}},v_2=2m\sqrt{\frac{2G}{2m}}


Answers (1)

best_answer

TE_1=TE_2

O=\frac{G(m)(2m)}{d}+\frac{1}{2}mv_1^2+\frac{1}{2}(2m)v_2^2

\frac{2Gm}{d}=\frac{1}{2}(v_1^2+2v_2^2)

\frac{4Gm}{d}=v_1^2+2v_2^2                            .......(1)

Initial momentum = Final momentum

0=mv_1+2mv_2

v_1=-2v_2

v_1=2m\sqrt{\frac{2G}{d(3m)}}, v_2=m\sqrt{\frac{2G}{d(3m)}}

Posted by

Suraj Bhandari

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