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Problem 24 Easy Difficulty

The weight of an object is the same on two different planets. The mass of planet $\mathrm{A}$ is only sixty percent that of planet $\mathrm{B}$ . Find the ratio $r_{N} / r_{\mathrm{B}}$ of the radii of the planets.

Answer

0.77

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Video Transcript

we begin this question by noting that the weight off an object on the surface off Planet A is equal to the weight off that same object at the surface on the planet be therefore D A Times M is equals two g b times the same mass. M done by Simply find the masses. We get the following G eight Izzy Coaster G. We now remember that the surface gravity often object, is given by Newton's constant times. The mass off that object divided by the radio's squared off the subject. So this relation implies that G. Newton's constant times the mass off Planet A divided by the radios off Planet A squared is because to the new terms, constant times the mass off planet be divided by the radios off Planet B squared then as D is a constant, we can simplify it. So we got that. The mass of Planet A, divided by the radios off planet A squared is equal to the mass offline. It be divided by the radios off definitely squared. Then we can sand are a to the other side multiplying and n b to the other side dividing. So we got em a divided by m Be easy goes to our a squared divided by r B squared But we know this information. The mass off planet A is equals 262% The mass of planet be therefore M A divided by EMI is he goes to 0.6 so 0.6 is equals. Two are a divided by RV squared then the Rachel are a divided by r B is equal to the square it off 0.6, which is approximately 0.77.