a body weighs 72 n on the surface of the earth. what is the gravitational force on it, at a height equal to half the radius of the earth?

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A body weighs 72 N on the surface of earth. What is the gravitational force on it due to earth at a height equal to half the radius of the earth from the surface?

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Question

A body weighs 72 N on the surface of earth. What is the gravitational force on it due to earth at a height equal to half the radius of the earth from the surface?

A

72 N

B

28 N

C

16 N

D

32 N

Medium Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Correct option is D)

At the surface of Earth, weight W=72N

∴F=mg=72N m= 10 72 ​ =7.2kg

Now, at some height, h acceleration due to gravity is given as

g ′ = (1+ R h ​ ) 2 g ​ Here, h= 2 R ​ g ′ = (1+ 2 1 ​ ) 2 g ​ = 9 4 ​ g=4.44m/s 2

Now, the force experienced by the body at half of the radius of the earth is given by:

F ′ =mg ′

=7.2×4.44=31.97N≈32N

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A body weighs 72 N on the surface of the earth. What is the gravitational force on it due to the Earth at a height equal to half the radius of the earth? (1) 48 n (2) 32 n (3) 30 n (4) 24 n Physics Q&A

A body weighs 72 N on the surface of the earth. What is the gravitational force on it due to the Earth at a height equal to half the radius of the earth? (1) 48 n (2) 32 n (3) 30 n (4) 24 n Get the answer to this question and access a vast question bank that is tailored for students.

Byju's Answer Standard VIII Physics

Universal Law of Gravitation

A body weighs... Question A body weighs 72 N

on the surface of the earth. What is the gravitational force on it due to the Earth at a height equal to half the radius of earth?

A 48 N B 32 N C 30 N D 24 N Open in App Solution

The correct option is B

32 N

Step 1: Given data

The weight of the body is

72 N .

The height of the body is

R2 .

Step 2: Gravitational force

The gravitational force of the earth is defined by the force exerted on a body due to the earth.

Gravitational force,

F=GmMR2

, where, M and m are the mass of the earth and the body respectively, G is the universal gravitational constant, and R is the radius of the earth.

Weight W is a gravitational force, which is equivalent to F.

Step 3: Finding the gravitational force

Gravitational force at a distance R (on the surface of the earth) is

F=GmMR2

which is equal to the body weight.

So,

F=GmMR2 ..................(1)

Now, gravitational force at a distance

R2

from the earth's surface is

F'=GmMR+R22=GmM3R22

or F'=G4Mm9R2 ..............(2)

Dividing equation 2 by equation 1

F'F=G4Mm9R2GMmR2=49 or F'=49×F=49×72 or F'=32 N

The gravitational force exerted on the body at a height is

32 N

. So, option (B) is correct.

Suggest Corrections 11

SIMILAR QUESTIONS

Q. A body weighs

63 N

on the surface of the earth. What is the gravitational force (in newton) on it due to the earth at a height equal to half the radius of the earth?

Q. A body weighs

72 N

on the surface of earth. What is the gravitational force on it due to earth at a height equal to half the radius of the earth from the surface?

Q. A body weight

72 N

on the surface of the earth. What is the gravitational force acting on it due to the earth at a height equal to half the radius of the earth from the surface?

EXPLORE MORE

Universal Law of Gravitation

Standard VIII Physics

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A body weighs 72 N on the surface of the earth. What is the gravitational force on it due to the Earth at a height equal to half the radius of the earth?A.)16 NB.)28 NC.)32 ND.)72 N

A body weighs 72 N on the surface of the earth. What is the gravitational force on it due to the Earth at a height equal to half the radius of the earth?A.)16 NB.)28 NC.)32 ND.)72 N. Ans: Hint: A good approach would be to determine the acceleration d...

A body weighs 72 N on the surface of the earth. What is the gravitational force on it due to the Earth at a height equal to half the radius of the earth?

A.)16 N B.)28 N C.)32 N D.)72 N

Last updated date: 19th Jan 2023

• Total views: 196.5k • Views today: 1.92k Answer Verified 196.5k+ views 6 likes

Hint: A good approach would be to determine the acceleration due to gravity from the universal law of gravitation for when the body is at the surface of the earth, and then find the acceleration due to gravity at a height h using the same law but in terms of g at surface. Formula used:

Acceleration due to gravity

g= GM R 2 g=GMR2

where G is the gravitational constant. M is the mass of the body exerting force and R is the distance to the body.

Force acting on a body due to gravitational acceleration

F=mg F=mg

where m is the mass of the body and g is the acceleration due to gravity

Complete answer:

Let us begin by looking at the first scenario:

On the surface of the Earth, i.e., at a height R (where R is the radius of the Earth),

F=mg=72N F=mg=72N .

From the universal law of gravitation we get:

F= GMm R 2 ⇒mg= GMm R 2 ⇒g= GM R 2

F=GMmR2⇒mg=GMmR2⇒g=GMR2

Now, if the body is raised to a height of

h= R 2 h=R2

then the acceleration due to gravity at that height will be:

g h = GM (R+h) 2 = GM (R+ R 2 ) 2 = 4 9 ( GM R 2 )⇒ g h = 4 9 g

gh=GM(R+h)2=GM(R+R2)2=49(GMR2)⇒gh=49g

Therefore, the gravitational force acting on the body at height h is found to be:

F h =m g h =m× 4 9 ×g= 4 9 ×mg= 4 9 ×72⇒ F h =32 N

Fh=mgh=m×49×g=49×mg=49×72⇒Fh=32N

Hence, the correct choice would be 32 N.

So, the correct answer is “Option C”.Note:

Remember that the weight of the body is basically the gravitational force acting on it, which is why it is safe to assume mg = 72 N.

When a body is raised to a certain height from the surface of the earth, do not forget to include the radius of the earth to the distance since the point of origin of this acceleration due to gravity is assumed to be the planetary centre. However, when

h<h<

where R is the earth radius then you can use the approximation :

g h = g 1− 2h R gh=g1−2hR .

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