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Chapter 13: Q. 6 (page 353)

The free-fall acceleration at the surface of planet 1 is 20 m/s2. The radius and the mass of planet 2 are twice those of planet 1. What is g on planet 2?

Short Answer

Expert verified

The value of g on planet 2 is : 10 m/s²

Step by step solution

01

Given Information

The free-fall acceleration at the surface of planet 1 is 20 m/s2

The radius and the mass of planet 2 are twice those of planet 1

02

Explanation

The free fall acceleration is calculated as below

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

g= acceleration due to gravity,

M =mass

G = universal gravitational constant

r= distance from the center of mass of body

role="math" localid="1649255660263" $\frac{g^{'}}{g} = \frac{G m}{r^{2}} \cdot \frac{R^{2}}{G M} g^{'} = g \frac{(2 M)}{(2 R)^{2}} \frac{R^{2}}{M} g^{'} = \frac{g}{2}$

Substitute the value

$g^{'} = \frac{20 m / s^{2}}{2} = 10 m / s^{2}$

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Most popular questions from this chapter

Two spherical asteroids have the same radius $R$ . Asteroid $1$ has mass $M$ and asteroid $2$ has mass $2 M .$ The two asteroids are released from rest with distance $10 R$ between their centers. What is the speed of each asteroid just before they collide?

Hint: You will need to use two conservation laws.

A new planet is discovered orbiting the star Vega in a circular orbit. The planet takes $55$ earth years to complete one orbit around the star. Vega’s mass is $2.1$ times the sun’s mass. What is the radius of the planet’s orbit? Give your answer as a multiple of the radius of the earth’s orbit.

An astronaut on earth can throw a ball straight up to a height of $15 m .$ How high can he throw the ball on Mars?

You have been visiting a distant planet. Your measurements have determined that the planet’s mass is twice that of earth but the free-fall acceleration at the surface is only one-fourth as large.

a. What is the planet’s radius?

b. To get back to earth, you need to escape the planet. What minimum speed does your rocket need?

Satellites in near-earth orbit experience a very slight drag due to the extremely thin upper atmosphere. These satellites slowly but surely spiral inward, where they finally burn up as they reach the thicker lower levels of the atmosphere. The radius decreases so slowly that you can consider the satellite to have a circular orbit at all times. As a satellite spirals inward, does it speed up, slow down, or maintain the same speed? Explain.

See all solutions

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