Question

Which of the following combinations is true about the mass of a body according to Newton?
I. Mass is the quantity of matter contained in a body
II. Mass is represented by the relation: mass $= \dfrac{{{\text{force}}}}{{{\text{velocity}}}}$
III. Mass is always conserved
IV. Mass of a body is the ratio of its weight to acceleration due to gravity at a particular place.
(A) I, II and IV only
(B) I, III and IV only
(C) I, II and III only
(D) I, II, III and IV

Answer 1

Mass is the amount of the substance in the body. It is called the weight when the body is also pulled by the gravitational force. For the second and the fourth statement, derive the mass from the formula of the force and the weight to find the correct statement.

Useful formula:
(1) The formula of the Newton’s second law of motion is given by
$F = ma$
Where $F$ is the force, $m$ is the mass of the body and the $a$ is the acceleration of the body.
(2) The formula of the mass is given by
$m = \dfrac{W}{g}$
Where $m$ is the mass of the body, $W$ is the weight and $g$ is the acceleration due to gravity.
Complete step by step by solution:
I. This states about the definition of the mass. That is the substance that is present in the body. The unit of the mass is kilogram. When it is accompanied by the gravitational force of the earth, it is called the weight. Hence this is correct.
II. We know that Newton's law of motion is $F = ma$ . From this the mass of the body is derived by dividing the force by the acceleration. Not as the force by the velocity. Hence this statement is not true.
III. Mass is conserved. This is given by the law of conservation of the mass. This states that the mass is neither created nor destroyed but it transforms from one form into the other forms. Hence this statement is also true.
IV. This statement says that the mass is obtained by dividing the weight of the body by the acceleration of the body. Hence the weight is the product of the mass and the acceleration due to gravity. Thus this statement is also true.

Thus the option (B) is correct.

Note: The mass of the body always remains constant. But the weight of it changes depending on the gravitational force. The earth’s gravity is six times less than the gravitational force of the earth. So the weight of the body reduces six times at the surface of the moon.