a planet has a mass of 6.49 x 10^25 kg and a radius of 2.1 x 10^7 meters. determine the gravitational field strength on the surface of the planet.

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Accepted Answer

# Explanation:
## Step1: Recall the formula for gravitational field strength
The formula for gravitational field strength $g$ on the surface of a planet is $g=\frac{GM}{R^{2}}$, where $G = 6.67\times10^{- 11}\space Nm^{2}/kg^{2}$ (universal gravitational constant), $M$ is the mass of the planet, and $R$ is the radius of the planet.
## Step2: Substitute the given values into the formula
Given $M = 6.49\times10^{25}\space kg$ and $R=2.1\times 10^{7}\space m$
$$
\begin{align*}
g&=\frac{6.67\times 10^{-11}\times6.49\times 10^{25}}{(2.1\times 10^{7})^{2}}\
&=\frac{6.67\times6.49\times10^{-11 + 25}}{2.1^{2}\times10^{14}}\
&=\frac{43.2\times10^{14}}{4.41\times10^{14}}
\end{align*}
$$
## Step3: Calculate the value of $g$
$$
g=\frac{43.2}{4.41}\approx9.8\space N/kg
$$

# Answer:
$9.8\space N/kg$

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Question

Explanation:

Step1: Recall the formula for gravitational field strength

Step2: Substitute the given values into the formula

Step3: Calculate the value of \(g\)

Answer: