Question

The masses and radii of Earth and Moon are M₁,R₁ and M₂, R₂ respectively. Their centre are at a distance d apart. The minimum speed with which a particle of mass m should be projected from a point mid-way between the two centres so as to escape to infinity is :

• A.
• B.
• C.
• D.

Answer 1

Answer: (D)

Answer 2

Total potential energy at mid point is

$\left[ - \frac { \mathrm { GM } _ { 1 } \mathrm {~m} } { \mathrm {~d} / 2 } - \frac { \mathrm { GM } _ { 2 } \mathrm {~m} } { \mathrm {~d} / 2 } \right]$

or – $\frac { 2 \mathrm { G } } { \mathrm { d } }$ (M₁ + M₂)m

If v is required escape velocity, the

$\frac { 1 } { 2 }$mv² = (M₁ + M₂)m

v =