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. During our discussion of the motion of a failing body near Earth’s surface, we said that the gravitational force acting on it—its weight—is constant. But the law of universal gravitation tells us that the gravitational force on a body increases as it gets closer to Earth. Is there a contradiction here? Explain. ( Hint : Calculate the gravitational force an a 1-kg mass located on Earth’s surface and then repeal the calculation for the same mass located 20 m above Earth’s surface. Compare your answers.)

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Inquiry into Physics

8th Edition
Ostdiek
Publisher: Cengage
ISBN: 9781337515863
Chapter 2, Problem 10C
Textbook Problem
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. During our discussion of the motion of a failing body near Earth’s surface, we said that the gravitational force acting on it—its weight—is constant. But the law of universal gravitation tells us that the gravitational force on a body increases as it gets closer to Earth. Is there a contradiction here? Explain. (Hint: Calculate the gravitational force an a 1-kg mass located on Earth’s surface and then repeal the calculation for the same mass located 20 m above Earth’s surface. Compare your answers.)

To determine

If there is a contradiction between the two statements −“The gravitational force acting on a body is a constant” and “ The gravitational force increases as it gets closer to Earth”.

Explanation of Solution

Given:

Mass of the object

m=1-kg

Radius of the Earth

R=6.4×106m

Mass of the earth

M=6.0×1024kg

Distance of the object from the surface of the earth

h=20 m

Universal gravitational constant

G=6.67×1011Nm2/kg2.

Formula used:

The gravitational force exerted on a mass m by the earth is given by,

F=GMmr2

Here, r is the distance between the object and the center of the earth.

Calculation:

(i) If the object is laced on the surface of the earth, then r=R.

Substitute the given values in the formula and calculate the gravitational force exerted on the mass.

F=GMmR2=(6.67×1011Nm2/kg2)(6.0×1024kg)(1-kg)(6.4× 10 6m)2=9

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