Answer:
F'=1/9*F0
Explanation:
F0 is the gravitational force between the particles. When the distance is triplicated we have that
[tex]F'=G\frac{m_1m_2}{(3r)^{2}}[/tex]
where r is the distance before the particles are separated, m1 and m2 are the masses their masses and G is the Canvendish's constant.
By some algebra we have
[tex]F'=\frac{1}{9}G\frac{m_1m_2}{r^2}=\frac{1}{9}F_0[/tex]
hope this helps!!
Answer:
Fâ = [tex]\frac{1}{9}[/tex]Fâ
Explanation:
Newton's law of universal gravitation states that the force of attraction or repulsion, F, between two particles of masses Mâ and Mâ is directly proportional to the product of these particles and inversely proportional to the square of the distance, r, between the two particles. i.e
F â MâMâ / r²
F = GMâMâ / r²       --------------------(i)
Where;
G is the constant of proportionality.
From equation (i), since the force is inversely proportional to the square of the distance, holding other variables constant, the equation can be reduced to;
F = k / r²
This implies that;
Fr² = k      -------------------(ii)
Now, according to the question;
F = Fâ
Substitute this into equation (ii) as follows;
Fâ r² = k    ----------------(iii)
Also, when the distance of separation, r, is trippled i.e r becomes 3r;
F = Fâ
Substitute these values into equation (ii) as follows;
Fâ(3r)² = k
9Fâr² = k         ---------------(iv)
Substitute the value of k in equation (iii) into equation (iv) as follows;
9Fâr² = Fâ r²       --------------(v)
Cancel r² on both sides of equation (v)
9Fâ = Fâ
Now make Fâ subject of the formula
Fâ = [tex]\frac{1}{9}[/tex]Fâ
Therefore, the new force Fâ = [tex]\frac{1}{9}[/tex]Fâ
