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Mass and Weight

Gravitation - Concepts

Mass

Weight

Acceleration Due To Gravity

Mass and Weight

Class - RRB Technician Grade I Signal Subjects

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,

$frac{W_m}{W_E}=frac{frac{mGM}{R^2}}{frac{100mGM}{16R^2}}=frac{16}{100}=frac{4}{25}=frac{1}{6}approx$ Thus, 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 $(w):=:mtimes:g$ Therefore, $w:= :70times9.8$

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

Amit's weight on earth's surface is 486N. His weight on the moon is
A. 486 N
B. 2916 N
C. 81 N
D. 0 N
Right Option : C
View Explanation

Question : 2

___________________ of an object is the force with which it is attracted towards the Earth.
A. Mass	B. Weight	C. Force	D. None of these.
Right Option : B
View Explanation

Question : 3

A planet has its radius and mass as twice and thrice, respectively to those of earth. If an object weighs 48N on the earth, its weight on that planet will be
A. 72N
B. 36N
C. 10N
D. 18N
Right Option : B
View Explanation