GravitationHard
Question
Two point objects of masses m and 4m are at rest at an infinite separation. They move towards each other under mutual gravitational attraction. If G is the universal gravitational constant, then at a separation r
Options
A.the total mechanical energy of the two objects is zero
B.their relative velocity is 
C.the total kinetic energy of the objects is 
D.their relative velocity is zero
Solution
By applying law of conservation of momentum 
mv1 - 4mv2 = 0 ⇒ v1 = 4v2
By applying conservation of energy
mv12 + 
4mv22 = 
⇒ 10mv22 = 
⇒ v2 = 2
∴ Total kinetic energy =
; Relative velocity for the particle ⇒ vrel = 
= 5v2 = 
OR
Mechanical energy of system = 0 = constant. By using reduced mass concept
μv2rel = 
where μ = 
m ⇒ vrel = 
Also total KE of system =
mv1 - 4mv2 = 0 ⇒ v1 = 4v2
By applying conservation of energy
mv12 + 4mv22 = ⇒ 10mv22 = ⇒ v2 = 2
∴ Total kinetic energy =
; Relative velocity for the particle ⇒ vrel = = 5v2 = OR
Mechanical energy of system = 0 = constant. By using reduced mass concept
μv2rel = where μ = m ⇒ vrel = Also total KE of system =
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