Auniform, solid, 1100.0 kg sphere has a radius of 5.00 m. find the gravitational force this sphere exerts on a 2.40 kgkg point mass placed at the following distances from the center of the sphere: (a) 5.01 mm , and (b) 2.50 mm .

Explanation:

(a)   The given data is as follows.

           M = 1100 kg,        r = 5.01 mm = m

          m = 2.40 kg

Now, formula for Newton's law of gravitation is as follows.

                 F =

Putting the given values into the above formula as follows.

               F =

                  =  

                  = N

Therefore, gravitational force exerted by the given sphere on 2.40 kg point mass is N.

(b) Now, mass of the sphere beyond r = 2.50 mm or will not contribute any force on the point mass.

Hence, mass within the radius r < R that experiences force is,

According to Newton's law of gravitation,

           F =

             =

             =

Here, r is the radius of point mass and R is the radius of solid sphere.

Therefore, putting the given values into the above formula as follows.

           F =

              =

              = N

Therefore, the gravitational force this sphere exerts on a 2.40 kg is N.

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