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!!

the minimum constant speed at which she can catch the train is 2.7 m/s

given:

acceleration = 0.6

time = 4.5 s

to find:

velocity = ?

formula used:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

solution:

from 1st kinematic equation we get,

v = u + at

u = initial speed of train = 0 m/s

v = final speed of the train

a = acceleration of the train

t = time

v = 0 + (0.6 × 4.5)

v = 2.7 m/s

the minimum constant speed at which she can catch the train is 2.7 m/s

because if the tool that you are using is not balanced it there would be false mass.