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Lubov Fominskaja [6]
2 years ago
9

The radius of a planet is 2400 km, and the acceleration due to gravity at its surface is 3.6 m/s2.

Physics
1 answer:
kiruha [24]2 years ago
6 0

Answer:

3.1\cdot10^{23}\:\mathrm{kg}

Explanation:

We can use Newton's Universal Law of Gravitation to solve this problem:

g_P=G\frac{m}{r^2}., where g_P is acceleration due to gravity at the planet's surface, G is gravitational constant 6.67\cdot 10^{-11}, m is the mass of the planet, and r is the radius of the planet.

Since acceleration due to gravity is given as m/s^2, our radius should be meters. Therefore, convert 2400 kilometers to meters:

2400\:\mathrm{km}=2,400,000\:\mathrm{m}.

Now plugging in our values, we get:

3.6=6.67\cdot10^{-11}\frac{m}{(2,400,000)^2},

Solving for m:

m=\frac{2,400,000^2\cdot3.6}{6.67\cdot 10^{-11}},\\m=\fbox{$3.1\cdot10^{23}\:\mathrm{kg}$}.

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