Discussion Forum

Two spherical planets P and Q have the same uniform density P, masses Mp and M_Q, and surface areas A and  4A, respectively. A spherical planet R also has uniform density ρ and its mass is (M_P + M_Q). The escape velocities from the planets P, Q and R, are V_P, V_Q^, and V_R, respectively. Then

Answer:

Explanation:

The surface area of Q is four times.
Therefore, radius of Q is two times. Volume is eight times. Therefore, mass of Q is also eight times.

 So, let $M_{p}=M$ and $R_{p}=r$

 Then, $M_{Q}=8M$ and $R_{Q}=2r$

 now, mass of  R is $(M_{p}+M_{Q})$ or 9M.

Therefore, radius of R is $(9)^{1/3}$ r. Now, escape velocity from the surface ofa planet  is given by

  $v=\sqrt{\frac{2GM}{r}}$

(r= radis of that planet)

$\therefore$   $v_{p}=\sqrt{\frac{2GM}{r}}$

$v_{Q}=\sqrt{\frac{2G(8M)}{(2r)}}$

$v_{R}=\sqrt{\frac{2G(9M)}{(9)^{1/3}r}}$

 from here we can see that,

  $\frac{v_{p}}{v_{Q}}=\frac{1}{2}$

 and  $V_{R}$ >$V_{Q}>$$V_{P}$