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An object with mass m is located halfway between an object of mass M and an object of mass 3M that are separated by a distance d. What is the magnitude of the force on the object with mass m?A) 8GMm/d^2B) GMm/(4d^2)C) 4GMm/d^2D) GMm/(2d^2)E) 3GMm/2d^2

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lublana

Answer:

A) 8GMm/d^2

Explanation:

We are given that

[tex]m_1=M[/tex]

[tex]m_2=3M[/tex]

[tex]m_3=m[/tex]

Distance between m1 and m2=d

Distance of object of mass m from m1 and m2=d/2

Gravitational force formula

[tex]F=\frac{Gm_1m_2}{r^2}[/tex]

Using the formula

Force acting between m and M is given by

[tex]F_1=\frac{GmM}{d^2/4}[/tex]

Force acting between m and 3M is given by

[tex]F_2=\frac{Gm(3M)}{d^2/4}[/tex]

Now, net force acting on  object of mass is given by

[tex]F=F_2-F_1[/tex]

[tex]F=\frac{Gm(3M)}{d^2/4}-\frac{GmM}{d^2/4}[/tex]

[tex]F=\frac{12GmM}{d^2}-\frac{4GmM}{d^2}[/tex]

[tex]F=\frac{12GmM-4GmM}{d^2}[/tex]

[tex]F=\frac{8GmM}{d^2}[/tex]

Hence, the magnitude of the force on the object with mass m=[tex]\frac{8GmM}{d^2}[/tex]

Option A is correct.

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