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    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?

    Click here👆to get an answer to your 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?

    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

    स्रोत : byjus.com

    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 .

    स्रोत : www.vedantu.com

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