The figure shows a system of five objects. Determine the magnitude of the gravitational force acting on the object placed in the middle of the square.

Select one:
O a. 4Gm2/d2
O b. Gm2/d2
O c. 8Gm2/d2

c.  

Explanation:

In order to calculate the gravitational force on the mass of the center, you take into account the following formula:

        (1)

Furthermore, you take into account the components of the resultant vector.

By the illustration, you have that the force is given by:

where:

m1 = m

m2 = 2m

m3 = m

m4 = 4m

m: mass at the center of the system

The distance r is:

You replace the values for all masses and sum the contributions of all forces:

and the magnitude is:

c.  

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