Please give me the answer in full detail!! Thankk youu!!

Question

The gravitational force (F) exetrted by one object and another is directly proportional to the mass (m) of the object and inversely proportional to the square of the distance (d) between the objects.

i State a relationship between F, m and d.

ii When m=4, d= 3 and F= 64. Find an equation connecting F, m and d.

iii Find the value of m when F = 480 and d= 9

iv Find the value of d when F = 57.6 and m =10

Find an equation connecting F, d.

Answer 1

i.

By definition of "directly proportional" and "indirectly proportional",

F = Km/d² (1)

where K is the constant of proportionality.

ii.

Substitute the three values into (1)

64 = 4K/3²

From that can calculate K:

K = 64×3²/4 = 144

Substitute K into (1)

F = 144m/d² (2)

iii.

From (2) express m

m = Fd²/144

Substitute actual numbers:

m = 480×9²/144 = 270

iv.

From (2) express d

d = √(144m/F)

Substitute actual numbers

d = √(144×10/57.6) = 5