Mass and Weight


 
 
Concept Explanation
 

Mass and Weight

Weight: of an object is the force with which it is attracted towards the Earth. Weight of an object, w = mg, where, m = mass, g = acceleration due to gravity.

w=frac{mGM}{R^2}

Here, M = mass of the earth and R radius of the earth

From the above formula, it is clear that weight of an object will change on a planet other than the earth. Spring balance is used to measure the weight of a body and pan balance is used to measure the mass of a body.

Important points regarding weight are as follow:

  • Weight is a vector quantity; it acts in vertically downward direction, and its SI unit is Newton (N). Weight of 1 kg mass is 9.8 N (i.e. 1 kg-wt=9.8N).
  • Weight of an object is not constant; it changes from place to place.
  • In the space, where g = 0, weight of an object is zero.
  • At the centre of the earth, weight becomes zero. This is due to the fact that on going down to the earth value of g decreases and at the centre of the earth, g = 0.
  • Weight of an Object on the Moon: Let the mass of an object be ‘m’ and its weight on the moon be  W_m. Suppose the mass of the moon is ‘M’ and its radius be ‘R’. According to universal law of gravitation, the weight of an object on the moon will be

    W_m=frac{mGM}{R^2}

    Let the weight of the same object on the earth be W_E. But the mass of the earth is 100 times that of the moon and the radius of the earth is 4 times that of the moon. Weight of the object on the earth,

    W_E=frac{100mGM}{(4R)^2}= frac{100mGM}{16R^2}On dividing these equations,

    frac{W_m}{W_E}=frac{frac{mGM}{R^2}}{frac{100mGM}{16R^2}}=frac{16}{100}=frac{4}{25}=frac{1}{6}approxThus, the weight of an object on the moon is one-sixth of its weight on the earth.

    Q.  A person's mass happens to be 70 kg, while the gravity on Earth is  9.8:m/s^2. Find out the weight of this person?

    Solution: Here, mass(m) = 70 kg and g = 9.8:m/s^2

    As we know that  weight  (w):=:mtimes:gTherefore,                         w:= :70times9.8

    Hence, the weight of the person  =   686 N

    Q. Conisder a heavenly body whose mass is twice that of the earth and whose radius is thrice that of the earth.What will be the weight of a book on this heavenly body, if its weight on the earth is 900 N ?

    Solution: The weight of the book on the earth is W:=:frac{GM_em}{R^2_e}

    If weight on the heavenly body is  W^*:=:frac{GM_e^*m}{R^*^2}

    Thus,                                             frac{W^*}{W}:=:frac{M^*R^2_e}{M_eR^*^2}:=:frac{2M_eR_e^2}{M_e(3R_e)^2}=frac{2}{9}

    or                                                    W^* :=;frac{2}{9}W:=:frac{2}{9}times(900 N):=:200N                                                 

    Sample Questions
    (More Questions for each concept available in Login)
    Question : 1

    Weight is a _______________ quantity and in the space, where g = 0, weight of an object is ________________.

    Right Option : A
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    Explanation
    Question : 2

    Which of the following are correct :

    (a) Weight of an object is the force with which it is attracted towards the Earth.

    (b) Weight of an object is not constant; it changes from place to place.

    (c) Weight of an object is constant; it cannot changes from place to place.

    Right Option : A
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    Explanation
    Question : 3

    Identify the correct statement.

    Right Option : A
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    Explanation
     
     
     


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