Question

Please Help!
Consider two uniform spherical planets of equal density but unequal radius. Which of the following quantities is the same for both planets?

Answer 1

(a) the escape velocity from the planet's surface
(b) the acceleration due to gravity at the planet's surface
(c) the orbital period of a satellite in a circular orbit just above the planet's surface
(d) the orbital period of a satellite in a circular obit at a given distance freom the planet's center

Answer 2

d

Answer 3

option c is right u have to go stepwise
first find the relation connecting R1, M1, R2 and M2 USING DATA DENSIOTY CONSTANT
then go on to check each of the options given using the mass andd radius relation u got
u will find that c is right
u will need:
g=GM/R^2
T=2*pi*R/V0
where V0 is orbitaol veloicity given by centripetal force
mV0^2/R=GMm/R^2

and escape velocity expression

Answer 4

as escape velocity,acceleration due to gravity and c; depends upon the radius of the planet and option d depends upon the distance between the center and the satellite, d is the correct option

Answer 5

its C.. C is right.. if you use the equation of orbital time period using keplers third law you get

\[T ^{2}= 4\pi ^{2}R ^{3}/GM \]

now \[R ^{3}/M\] is a constant for both planets (cause density is same).. and all other parameters also constant.. thus they both got same orbital period

D however is wrong because.. in d equation would become \[T ^{2}= 4\pi ^{2}(R+h) ^{3}/GM \].. and \[(R+h) ^{3}/M \] need not be a constant for both the planets.. ARggg this equation thing is such a headache :-/