Question

What is the mass of an object whose weight is $980N$ ?
(A) $980kg$
(B) $98kg$
(C) $100kg$
(D) Zero

Answer 1

To solve this question, we have to 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: The formula which is used to solve this question is given by
$F = ma$, here $F$ is the force acting on an object of mass $m$ which is having an acceleration of $a$.

Complete step by step answer
We know that the weight of an object on a planet is nothing but the force of gravitation that the planet exerts on that object. 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 gravity of the planet. 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 equal to $980N$. So we substitute $F = 980N$ above to get
$980 = mg$
Now, we know that the value of the acceleration due to gravity for the earth is equal to $9.8m/{s^2}$. Therefore substituting $g = 9.8m/{s^2}$ above we get
$980 = 9.8m$
$\Rightarrow m = \dfrac{{980}}{{9.8}}kg$
On solving we get
$m = 100kg$
Thus, the mass of the object is equal to $100kg$.

Hence, the correct answer is option C.

Note
We should not use the value of the acceleration due to gravity for the earth as $10m/{s^2}$. Although it is a familiar value, it is only used for the convenience unless stated in the question. Since the value of the acceleration due to gravity was not given in the question, we took it to be equal to $9.8m/{s^2}$, which is the exact value.