Question

If our moon was twice as far away and had twice as much mass as it now has, how would its new speed compare to its present speed?

• A. The new speed would be half as much as the present speed
• B. The new speed would be smaller, but more than half the present speed
• C. The new speed would be one-fourth the present speed
• D. The new speed would be greater than the present speed
• E. The new speed would be the same as the present speed

Answer 1

The correct option is B The new speed would be smaller, but more than half the present speed

Orbital speed of moon initially $v=\sqrt{\frac{GM}{r}}$

where $M$ is the mass of earth and $r$ is the distance of moon from earth

$⟹$ Velocity of moon is independent of mass of moon $\left(m\right)$.

Now the mass and distance of moon from earth are doubled i.e $m^{\prime }=2m$ and $r^{\prime }=2r$

$\therefore$ New speed of moon $v^{\prime }=\sqrt{\frac{GM}{2r}}=\frac{v}{\sqrt{2}}=0.707v$

Thus option B is correct.