Question

Two bodies of masses m₁ and m₂ are initially at rest placed infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity when they are r distance apart is –

• A.
• B. $\sqrt { \frac { 2 \mathrm { Gm } _ { 1 } \mathrm {~m} _ { 2 } } { \left( \mathrm {~m} _ { 1 } + \mathrm { m } _ { 2 } \right) \mathrm { r } } }$
• C.
• D.

Answer 1

Answer: (A)

Answer 2

m₁v₁ – m₂v₂ = 0 by conservation of momentum

$\frac { 1 } { 2 }$m₁v₁² + $\frac { 1 } { 2 }$m₂v₂² – = 0

(by conservation of energy)

Also, v_rel. = v₁ + v₂