Two spheres of masses m = 1.09 g and m' = 1.03*10^2 kg are isolated from all other bodies and are initially at rest, with their centers a distance r = 14 cm apart. One minute later, the smaller sphere has moved 0.500 mm toward the larger sphere. Compute the acceleration and the value of G

To compute the acceleration and the value of the gravitational constant G, we can use Newton's law of gravitation. The law states that the force between two objects with masses m1 and m2, separated by a distance r, is given by:

F = G * (m1 * m2) / r^2

where G is the gravitational constant.

First, let's compute the force between the two spheres using the information given. The smaller mass is m = 1.09 g, which is equal to 1.09 * 10^-3 kg (converting grams to kilograms). The larger mass is m' = 1.03 * 10^2 kg. The distance between the centers of the spheres is r = 14 cm, which is equal to 14 * 10^-2 m (converting centimeters to meters).

Plugging these values into Newton's law of gravitation, we have:

F = G * (m * m') / r^2

Next, we need to compute the acceleration. Newton's second law of motion states that force is equal to mass multiplied by acceleration (F = m * a). Since the smaller mass has moved towards the larger sphere, we can assume that it is experiencing an attractive force towards the larger sphere.

Therefore, we can set F equal to the net force acting on the smaller sphere. And since the smaller sphere is experiencing this attractive force in the direction of the larger sphere, we can write:

F = m * a

Combining these two equations, we have:

G * (m * m') / r^2 = m * a

Now we can solve for the acceleration (a):

a = (G * m' / r^2)

Using the given values, we can substitute them into the equation to find the acceleration.

Now, let's compute the value of G. Rearranging the equation above, we have:

G = (a * r^2) / m'

Substituting the values from the problem, we can calculate G.

So, to summarize:
1. Compute the force using Newton's law of gravitation: F = G * (m * m') / r^2.
2. Compute the acceleration using F = m * a: a = (G * m') / r^2.
3. Compute the value of G using G = (a * r^2) / m'.

Plug in the given values in each step to get the final answers for acceleration and G.