Question

What is the mass of a body whose weight is $59N$? Take $g = 9.8m{\text{ }}{{\text{s}}^{ - 2}}$.

Answer 1

To solve this question, we must use the relation between the mass of an object with its weight on the earth. Then substituting the value of the acceleration due to gravity for the earth, we can get the required value of the mass of the mass of the given object.

Formula used:
$F = ma$
Where,
$F$is the force acting on the object,
$m$is the mass of the object and
$a$is the acceleration due to gravity.

Complete step by step solution:
As we know that the weight of an object is the force acting on the object due to gravity. The force of gravitation is given by the Newton’s law of gravitation as,
$F = \dfrac{{GMm}}{{{r^2}}}$
Now, the quantity $\dfrac{{Gm}}{{{r^2}}}$ is equal to the acceleration due to the gravity So substituting $\dfrac{{Gm}}{{{r^2}}} = g$ in the above equation we get,
$F = mg$
According to the question, the weight of the object is $59N$ . So, we put $F = 59N$ in above we get,
$59 = mg$
And it is given that $g = 9.8m{\text{ }}{{\text{s}}^{ - 2}}$.
$\therefore 59 = m \times 9.8 \\\ \Rightarrow m = \dfrac{{59}}{{9.8}} \\\ \Rightarrow m = 6.0204..... \\\ \therefore m = 6kg \\\$
So, the mass of a body whose weight is $59N$ is $6kg$.

Additional information:
Your mass is the same no matter where you go in the universe; your weight, on the other hand, changes from place to place. Mass is measured in kilograms; even though we usually talk about weight in kilograms, strictly speaking it should be measured in newtons.

Note:
In this type of question, we should not use $g = 10$as it will give you inappropriate results, as the value $g = 10$ is used for convenience purposes only. And only use when the value is provided in question as in this question it is given that take $g = 9.8m{\text{ }}{{\text{s}}^{ - 2}}$.