Question

Three masses, m1 (a mouse), m2 (a bear) and m3 (an elephant), are in circular orbits of radii r1, r2 and r3 around the sun. The masses obey the relation, m1 < m2 < m3. While r1 and r2 are equal to Earth's orbital radius, r3 is equal to Jupiter's orbital radius.


1) The orbital period of m3 is ____________________ the orbital period of m2.
A) greater than


2) The orbital period of m2 is ____________________ the orbital period of m1.
A) equal to


3) The magnitude of the acceleration of m2 is _____________ the magnitude of the acceleration of m1.
A) equal to

4) The magnitude of the gravitational force acting on m2 is ____________________ the magnitude of the gravitational force acting on m1.
A) greater than



How do you figure out 4? And, I got the other 3 correct but I'm not sure if I just guessed lucky.

What's the best way to do this?

Answer 1

all correct.
One way to think on four is to stop considering "g" as acceleration as in three. In the equation
gravitational force= mass*g
consider g to be gravitational field strength, in newtons/kg. In Earths case, g at the surface is 9.8N/kg

Using this thinking, then if the mass m2>m1, gravitational force= m2*g , so the force on m2 is greater than on m1 because its mass is greater.

Answer 2

In 4, both masses are the same distance from the (same) sun. Force is proportional to mass, so m2 has the greater force from the sun.