Answer:
the new gravitational force between the two masses is [tex]\frac{3}{2}[/tex] of the original force (third option in the provided list)
Explanation:
Recall the expression for gravitational force : [tex]F_g=G\,\frac{m_A*\,m_B2}{d^2}[/tex], where [tex]m_A[/tex] and [tex]m_B[/tex] are the point masses, d the distance between them, and G the universal gravitational constant.
I our problem, the distant between the particles stays unchanged, and we need to know what happens with the magnitude of the force as mass A is tripled, and mass B is halved.
Initial force expression: [tex]F_i=G\,\frac{m_A\,m_B}{d^2}[/tex]
Final force expression: [tex]F_f=G\,\frac{3*m_A\,m_B/2}{d^2}\\F_f=G\,\frac{m_A\,m_B\,*\,3/2}{d^2}\\F_f=G\,\frac{m_A\,m_B}{d^2}\,*\frac{3}{2} \\F_f=F_i\,*\frac{3}{2}[/tex]
Where we have recognized the expression for the initial force between the particles, and replaced it with [tex]F_i[/tex] to make the new relation obvious.
Therefore, the new gravitational force between the two masses is [tex]\frac{3}{2}[/tex] of the original force.
