Two uniform spherical bodies of masses 2M and M and of radii 3R and R, respectively, are held at a - Physics - Gravitation

Question

Two uniform spherical bodies of masses 2M and M and of radii 3R and
R, respectively, are held at a distance 16R from each other in free
space When they are released, they start approaching each other due
to gravitational force of attraction Then, find

(a) the ratio of their accelerations during their motion
(b) their velocities at the time of impact

Ravi Gupta · Accepted Answer

Dear Student
Kindly find the answer of your asked query

(a) Gravitational force between them is given by:F=GM1M2r2force acting of mass 2M is given by:F1=2Ma1=G2MMr2a1=GMr2similarlly force acting of mass M is given by:F2=Ma2=G2MMr2a2=G2Mr2a1a2=GMr2G2Mr2=12(B) since this is the concept of variable force hence work done is  given by:hence potential energy will be  equal to the chage in kinetic energy-∫16R4RGM1M2r2dr GM1M21-1r16R4RGM1M214R-116R3GM1M216Rfor mass 2M,122Mv12-0=3G2MM16Rv1=3GM8Rsimilarlyv2=3G×2M8Rv1v2=12

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