Astronomers observe two separate solar systems each consisting of a planet orbiting a sun. The two orbits are circular and have the same radius R. It is determined that the planets have angular momenta of the same magnitude L about their suns, and that the orbital periods are in the ratio of three to one; i. e., T1 = 3T2. The ratio m1/m2 of the masses of the two planets is

(A) 1
(C) (3)^1/2
(C) 2
(D) 3
(E) 9

(D) 3

Explanation:

The angular momentum is given by:

Thus, the magnitude of the angular momenta of both solar systems are given by:

where we have taken that both systems has the same radius.

By taking into account that T1=3T2, we have

but L1=L2=L:

Hence, the answer is (D) 3

HOPE THIS HELPS!!

d₁ = displacement of tern from arctic to antarctic = 11000 miles

d₂ = displacement of tern from antarctic to arctic =   - 11000 miles

d = total displacement for the journey

total displacement for the journey is given as

d = d₁ + d₂

d = 11000 + (-11000)

d = 0 miles

t₁ = time of travel from arctic to antarctic = 3 months = 3 x 30 days = 90 days

t₂ = time of travel from antarctic to arctic = 3 months = 3 x 30 days = 90 days

t = total time of travel

total time of travel is given as

t = t₁ + t₂

t = 90 + 90

t = 180 days

average velocity is given as

average velocity = total displacement/ total time

v = d/t

v = 0/180

v = 0 miles/day