Question

The gravitational attraction between a 20 kg cannonball and a 0.002 kg

marble separated center-to-center by 0.30 m. Compute the gravitational
force of the marble.

Answer 1

`2.966* 10^(-11)\ N`

Step-by-step explanation:

Given:

Mass of the cannonball (M) = 20 kg

Mass of the marble (m) = 0.002 kg

Distance between the cannonball and marble (d) = 0.30 m

Universal gravitational constant (G) =
`6.674* 10^(-11)\ m^3 kg^(-1) s^(-2)`

Now, we know that, the gravitational force (F) acting between two bodies of masses (m) and (M) separated by a distance (d) is given as:

`F=(GMm)/(d^2)`

Plug in the given values and solve for 'F'. This gives,

`F=((6.674* 10^(-11)\ m^3 kg^(-1) s^(-2))* (20\ kg)* (0.002\ kg))/((0.30\ m)^2)\\\\F=(6.674* 20* 0.002* 10^(-11)\ m^3 kg^(-1+2) s^(-2))/(0.09\ m^2)\\\\F=2.966* 10^(-11)\ kg\cdot m\cdot s^(-2)\\\\F=2.966* 10^(-11)\ N.........(1\ N = 1\ kg\cdot m\cdot s^(-2))`

The same force is experienced by both cannonball and marble.

Therefore, the gravitational force of the marble is
`2.966* 10^(-11)\ N`