Answer:
-1.927 × 10^-4 N/m.
Explanation:
From Newton's law, F is proportional to 1/r^2, taking the derivative in respect to r of both sides of the equation
F = (2.99x10^16)/r^2
So you do that and you get
dF/dr = -2(2.99 × 10 ^16)/(r^3)
Given:
r = 6.77×10^6 m
dF/dr = -2(2.99 × 10 ^16)/(6.77×10^6)^3
= -1.927 × 10^-4 N/m.
The rate of change of force is mathematically given as
dF/dr= -1.927 e-4 N/m.
Generally from the Newton's law
F = (2.99x10^16)/r^2
Where
[tex]F=\frac{1}{r^2}[/tex]
Therefore
[tex]dF/dr = \frac{-2(2.99 × 10 ^16)}{(r^3)}[/tex]
Therefore
[tex]dF/dr =\frac{ -2(2.99 × 10 ^16)}{(6.77×10^6)^3 }[/tex]
dF/dr= -1.927 e-4 N/m.
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