## Q. 7.10

CERES

GOAL Relate Newton’s universal law of gravity to $m g$ and show how $g$ changes with position.

PROBLEM An astronaut standing on the surface of Ceres, the largest asteroid, drops a rock from a height of $10.0 \mathrm{~m}$. It takes $8.06 \mathrm{~s}$ to hit the ground. (a) Calculate the acceleration of gravity on Ceres. (b) Find the mass of Ceres, given that the radius of Ceres is $R_C=5.10 \times 10^2 \mathrm{~km}$. (c) Calculate the gravitational acceleration $50.0 \mathrm{~km}$ from the surface of Ceres.

STRATEGY Part (a) is a review of one-dimensional kinematics. In part (b) the weight of an object, $w=m g$, is the same as the magnitude of the force given by the universal law of gravity. Solve for the unknown mass of Ceres, after which the answer for (c) can be found by substitution into the universal law of gravity, Equation 7.21.

$F = G \frac{m_1 m_2}{r^2}$      [7.21]

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The text passage contains a physics problem with multiple parts (a, b, c) that involve calculations and the application of Newton’s universal law of gravity. The problem is described, and a strategy for solving it is provided, but no answers are given.
multiple_questions
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
## Q. 7.10

CERES

GOAL Relate Newton’s universal law of gravity to $m g$ and show how $g$ changes with position.

PROBLEM An astronaut standing on the surface of Ceres, the largest asteroid, drops a rock from a height of $10.0 \mathrm{~m}$. It takes $8.06 \mathrm{~s}$ to hit the ground. (a) Calculate the acceleration of gravity on Ceres. (b) Find the mass of Ceres, given that the radius of Ceres is $R_C=5.10 \times 10^2 \mathrm{~km}$. (c) Calculate the gravitational acceleration $50.0 \mathrm{~km}$ from the surface of Ceres.

STRATEGY Part (a) is a review of one-dimensional kinematics. In part (b) the weight of an object, $w=m g$, is the same as the magnitude of the force given by the universal law of gravity. Solve for the unknown mass of Ceres, after which the answer for (c) can be found by substitution into the universal law of gravity, Equation 7.21.

$F = G \frac{m_1 m_2}{r^2}$      [7.21]

The "Step-by-Step Explanation" refers to a detailed and sequential breakdown of the solution or reasoning behind the answer. This comprehensive explanation walks through each step of the answer, offering you clarity and understanding.
Our explanations are based on the best information we have, but they may not always be right or fit every situation.
The blue check mark means that this solution has been answered and checked by an expert. This guarantees that the final answer is accurate.

Question: 7.13

Question: 7.12

Question: 7.11

Question: 7.9

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Question: 7.6

Question: 7.AP.2

Question: 7.5

Question: 7.4
user
The text passage contains a physics problem with multiple parts (a, b, c) that involve calculations and the application of Newton’s universal law of gravity. The problem is described, and a strategy for solving it is provided, but no answers are given.

TYPE: MULTIPLE_QUESTIONS