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Chapter 13: Q19P (page 380)

what altitude above Earth’s surface would the gravitational acceleration be4.9m/s2?

Short Answer

Expert verified

The altitude above the earth’s surface where g is4.9m/s2 is2.6×106m

Step by step solution

01

The given data

The gravitational accelerationag=4.9m/s2

02

Understanding the concept of Gravitational acceleration

We use the concept of gravitational acceleration which is in terms of G, M, and r. We can write the equation for gravity at height h then we can solve it for h.

Formula:

Gravitational Acceleration, ag=GMr2 (i)

03

Calculation of the altitude above the Earth’s surface

We can write equation (i) using height h,

ag=GMRe+h2Re+h=GMagh=GMag-Re................(1)

Substituting the values of mass & radius of the Earth in equation (1), we get

h=(6.67×10-11)(5.97××1024)4.9-(6.37×106)h=2.6×106m

The altitude above Earth’s surface is at2.6×106m

Using Newton’s law of gravitation, we can find the height h where value of ‘g’ reduces to half its original value.

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Most popular questions from this chapter

In Problem 1, What ratio m / Mgives the least gravitational potential energy for the system?

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