Question

the radius of planet a is half the radius of planet b. if the mass of a is ma, what must be the massof b (mb) so that the value of g on b is half that of its value on a?

Answer 1

Planet B must have twice the mass of Planet A (mb = 2ma) for its gravitational acceleration (g) to be half of that on Planet A, assuming both planets have the same density.

Step-by-step explanation:

To find what mass Planet B (mb) must have so that its gravitational acceleration (g) is half that of Planet A, we use Newton's law of universal gravitation. Gravitational acceleration on the surface of a planet is given by the formula g = Gm/r², where G is the gravitational constant, m is the mass of the planet, and r is the radius of the planet.

Since the radius of Planet A is half that of Planet B, we can denote the radius of Planet A as r and that of Planet B as 2r. If the gravitational acceleration on B is half that on A, we have gB = 1/2gA. Substituting this into the equations for gravitational acceleration, we get:

gA = Gma/r²

gB = Gmb/(2r)² = Gmb/4r²

From gB = 1/2gA, we can derive:

Gmb/4r² = 1/2(Gma/r²)

Solving for mb, we find:

mb = 2ma

Therefore, the mass of Planet B must be twice the mass of Planet A for gravitational acceleration on B to be half of that on A, assuming their densities are homogeneous.