A group of astronauts lands on an unknown planet of radius 6.00 x 106 m. They drop a testmass from 5 m high and notice it takes 1.0 s to hit the ground. What is the mass of theunknown planet?a) 3.8 x 1024 kgb) 4.2 x 1024 kgc) 5 x 1024 kgd) 5.4 x 1024 kge) 5.8 x 1024 kg

Answered: A group of astronauts lands on an…

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter13: Gravitation

Section: Chapter Questions

Problem 28P: A body on the surface of a planet with the same radius as Earth’s weighs 10 times more than it does...

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Question

A group of astronauts lands on an unknown planet of radius 6.00 x 106 m. They drop a test
mass from 5 m high and notice it takes 1.0 s to hit the ground. What is the mass of the
unknown planet?
a) 3.8 x 1024 kg
b) 4.2 x 1024 kg
c) 5 x 1024 kg
d) 5.4 x 1024 kg
e) 5.8 x 1024 kg

Expert Solution

Step 1 :Introduction

According to Newton's laws of motion ,the distance travelled is calculated by using the formula $s = u t + \frac{1}{2} g t^{2}$ , where $u = 0 m / s$ is the initial velocity , $g$ is the acceleration due to gravity , $s = 5 m$ is the distance and $t = 1 s$ is the time taken .

The acceleration due to gravity is calculated by using the formula $g = \frac{G M}{r^{2}}$ , where $G = 6.67 \times 10^{- 11} m^{3} / k g s^{2}$ is the gravitational constant , M is the mass of the planet and $r = 6 \times 10^{6} m$ is the radius of the planet .

Step 2 :Calculation of the acceleration due to gravity

Calculate the acceleration due to gravity by using the formula $s = u t + \frac{1}{2} g t^{2}$ , where $u = 0 m / s$ is the initial velocity , $g$ is the acceleration due to gravity , $s = 5 m$ is the distance and $t = 1 s$ is the time taken .

$\begin{array}{rcl} s & = & u t + \frac{1}{2} g t^{2} \\ = & 0 + \frac{1}{2} g t^{2} \\ g & = & \frac{2 s}{t^{2}} \\ = & \frac{2 \times (5 m)}{{(1 s)}^{2}} \\ = & 10 m / s^{2} \end{array}$

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