Question

Two objects of masses m and 4m are at rest at an infinite separation. They move towards each other under mutual gravitational force of attraction. If G is the universal gravitational constant. Then at separation r

• A. the total energy of the two objects is zero
• B. their relative velocity of approach is ${\left(\frac{10Gm}{r}\right)}^{\frac{1}{2}}$
• C. the total kinetic energy of the objects is $\frac{4G{m}^2}{r}$
• D. net angular momentum of both the particles is zero about any point

Answer 1

Answer: (A), (C), (D)

The correct options are
A the total energy of the two objects is zero
C the total kinetic energy of the objects is $\frac{4G{m}^2}{r}$
D net angular momentum of both the particles is zero about any point

At the distance of r the mechanical energy of the system is given by

$\frac{1}{2}4m{v}^2+\frac{1}{2}m{v}^2-\frac{4G{m}^2}{r}=0,k_{total}=\frac{4G{m}^2}{r}$

$\therefore$ (A), (C) and (D)