Two spherical planets and have the same uniform density

PHYSICS · Single correct · A Level · Physics · Fields and their consequences · Fields and their consequences

Problem

Two spherical planets

P

and

Q

have the same uniform density

\rho

, masses

M_P

and

M_Q

and surface areas

A

and

4A

respectively. A spherical planet

R

also has uniform density

\rho

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 [2012] (1)

V_Q > V_R > V_P

(2)

V_R > V_Q > V_P

(3)

V_R / V_P = 3

(4)

V_P / V_Q = \frac{1}{2}