You stand on the surface of a mysterious planet with a mass of 6 ×10 24 kg and measure the surface gravity to be 7 m/s 2 . What must the radius of the planet be?

Alright guys, let's check out this example here. So we're standing on the surface of a planet and we're told the mass of that planet is and we're asked for the radius of this planet, assume that the surface gravity is something. So what we're really looking for is the radius of the planet. What is that variable? Is that little r? Is it h? Is it big r? Remember that is the radius of the planet. That's not a distance. So that is big r. So we're gonna be looking for that. What else are we told? We're told that the surface gravity is equal to 7 meters per second squared. Now whenever you see surface gravity and acceleration, we're always gonna use the g surface equation. So we're gonna need g. G surface is equal to big G, big M over big R squared. So this is where our our big R is gonna come from. All we need to do is just make sure that we have g, we have big m, and we have g surface. So we know that g is just a constant. We know that m is just the mass which is given to us right here, and the acceleration due to gravity is 7. So we've got that. So let's go ahead and just plug everything in. Actually, well, first of all, let's just rearrange things. We want r, so we're gonna have to move this thing over to the other side. So r is gonna have to go over here, and then g surface is gonna have to go down there. They're just gonna trade places. Right? So we've got r squared equals gm over g surface. So then we've got 6.67 times 10 to the minus 11, times the mass of the planet, 6 times 10 to the 24th. That's that's a 6. 6 times 20 to 24. And then we've got g surface, which is 7 meters per second. If you go ahead and do that, you're gonna get a number that is 5 point 72 times 10 to the 13th. Are we done? Well, no, not quite because we have to get the square root of this number. Right? We've just got r squared. So you take the square root, you should get r equals 7.56 times 10 to the 6th, and that's in meters. So that is the final answer for the radius. Let me know if you guys have any questions.

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8. Centripetal Forces & Gravitation

Acceleration Due to Gravity

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Multiple Choice

You stand on the surface of a mysterious planet with a mass of 6 ×10²⁴ kg and measure the surface gravity to be 7 m/s². What must the radius of the planet be?

5.72×10¹³m

4.43×10¹⁴m

8.17×10¹²m

7.56×10⁶m

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Verified step by step guidance

Start by recalling the formula for gravitational acceleration at the surface of a planet:

g = \frac{G M}{R^{2}}

, where

g

is the surface gravity,

G

is the gravitational constant,

M

is the mass of the planet, and

R

is the radius of the planet.

Rearrange the formula to solve for the radius

R

R = \sqrt{\frac{G M}{g}}

Substitute the known values into the equation:

G = 6.674 × 10

^-11 m³ kg^-1 s^-2,

M = 6 × 10

²⁴ kg, and

g = 7 m/s

².

Calculate the expression inside the square root:

\frac{G M}{g}

Finally, take the square root of the result from the previous step to find the radius

R

5:20m

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Struggling with Physics?

You stand on the surface of a mysterious planet with a mass of 6 ×1024 kg and measure the surface gravity to be 7 m/s2. What must the radius of the planet be?

Watch next

Acceleration Due to Gravity practice set

You stand on the surface of a mysterious planet with a mass of 6 ×10²⁴ kg and measure the surface gravity to be 7 m/s². What must the radius of the planet be?