a turtle has a mass of 10kg. if earths mass is 6 x 10^{24} kg and its radius is 6.4 x 10^{6} kg, what is the weight of the turtle?

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for gravitational force
The formula for gravitational force $F = G\frac{Mm}{r^{2}}$, where $G = 6.67\times10^{- 11}\space Nm^{2}/kg^{2}$, $M$ is the mass of the Earth, $m$ is the mass of the turtle, and $r$ is the radius of the Earth.
## Step2: Substitute the given values into the formula
Substitute $G = 6.67\times10^{-11}\space Nm^{2}/kg^{2}$, $M = 6\times10^{24}\space kg$, $m = 10\space kg$, and $r = 6.4\times10^{6}\space m$ into $F = G\frac{Mm}{r^{2}}$.
$$
\begin{align*}
F&=(6.67\times 10^{-11})\frac{(6\times 10^{24})\times(10)}{(6.4\times 10^{6})^{2}}\
&=(6.67\times 10^{-11})\frac{6\times10^{25}}{4.096\times 10^{13}}\
&=(6.67\times 10^{-11})\times(1.465\times10^{12})\
&=6.67\times1.465\times10^{-11 + 12}\
&=9.77\times10^{1}\
&\approx98\space N
\end{align*}
$$

# Answer:
The weight of the turtle is approximately $98\space N$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for gravitational force

Step2: Substitute the given values into the formula

Answer: