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Answers
Answer:
since there is no external force on the system. So total energy will be conserved.
(Total energy) state l =( Total energy) state ll
==> -Gmm'/1 = 0.5 mv^2 + 0.5 mv * 2-Gmm'/0.5
==> -Gmm' = 1/2(mv^2 + m'v'^2) - 2Gmm'
==> 1/2(mv^2 + m'v'^2) = Gmm'
==> (mv^2 + m'v'^2) = 2Gmm'..............................(1)
Here v = velocity of smaller mass(m= 20kg)
v' = velocity of bigger mass( m' = 20kg)
Also momentum of the system will be conserve initial momentum = final momentum
==> O = mv - m'v ( Because both are moving in opposite direction)
==> mv = m'v'
v/v¹=m¹/m
==> v = 2v'......................................(2)
put in v = 2v' in eq. (1)
m(2v')^2 + m'v'^2 = 2G mm'
==>10 * 4v'^2 + 20v'^2 = 2*G (10)*(20)
==> 60v^2 = G 2*200
v²=(20/3)G
(20/3)*6.67*10-¹¹
v`=√6.66*6.67*10-¹¹
2.1*10-5m/s
=4.2*10-5(exponent *5)
so v = 2v'
Here's your answer in the given attachment
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