Determine the small gravitational force F which the copper sphere exerts on the steel sphere. Both spheres are homogeneous, and the value of r is 50 mm. Express your result as a vector.

Solution :

We know that the volume of sphere is given by :

Given r = 50 mm

The density of copper is :

The density of steel is :

Therefore, mass of copper is :

     = 4.665 kg

     = 4665 g

Similarly, mass of steel is :

     = 0.512 kg

     = 512 g

Now the distance between the centers of the particles is by Pythagoras theorem,

l = 4.472 x r

 = 4.472 x 50

 = 224 mm

 = 0.224 m

From the law of gravitation,

We know,  

∴  

Now,

   =  

Therefore, we can write it in the vector form as

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