Question

Calculate the weight of a body of mass $10kg$ , in (a) $kgF$ and in (b) Newton. Take $g=9.8m{{s}^{-2}}$.

Answer 1

Weight of a body is the force exerted on the body due to gravity. The International System of units defined the unit of weight measurement same as that of force which is Newton. The kilogram-force is a non-standard gravitational metric unit of force.

Complete step-by-step solution:
Kilogram-force of a body, abbreviated as $kgF$ is the weight of a kilogram under standard gravity.
Therefore, one kilogram-force is equivalent to $9.8N$ .
Weight of a body of mass $mkg$ is the force of earth’s gravity acting on that body.
As per the given problem, we are aware that the mass of the body is $10kg$ .
The weight of the body is given by,

& W=mg \\\ & \Rightarrow W=10\times 9.8 \\\ & \Rightarrow W=98kg.m.{{s}^{-2}} \\\ \end{aligned}$$ We also know that $$1kg.m.{{s}^{-2}}=1N$$ Hence the weight of the body in Newton will be $$98N$$ . We’ve stated before that $$1kgF=9.8N$$ . This means that $$1N$$ is equivalent to $$\frac{1}{9.8}kgF$$ Therefore, when we say that the weight of our body is $$98N$$ , we can also say that the weight of our body is $$\frac{1}{9.8}\times 98kgF=10kgF$$ . **Note:-** There is an obvious confusion between the mass of a body and the weight. The mass of a body is the measure of the amount of substance it contains and it does not vary with the place of measurement. Weight on the other hand is the measure of gravitational force acting on a body and varies as the acceleration due to gravity varies with the place of measurement.