# Mass and weight

Physical quantity of mass is kilo gram and weight is Newton but generally we say my weight is some x kg why so why does this confusion if I was not wrong weight=mass*acceleration due to gravitation But some of the physics books also I find this mistake they ask if a man weights 60 kg on earth what is his weight on moon the answer is 10 kg the explanation is moons acceleration is 1/6 of acceleration due gravity on earth please explain.

• You are confusing weight, mass and acceleration due to gravity. All three are different things. The mass is always the same and see formula for acceleration due to gravity. As for weight it depends on both of the above and whatever unit of measurement you are using. – Bill Alsept Oct 5 '16 at 18:35
• Possible duplicates: physics.stackexchange.com/q/43195/2451 , physics.stackexchange.com/q/138293/2451 and links therein. – Qmechanic Oct 5 '16 at 18:39
• It is a confusing issue, and your textbook is not helping the situation. We have the bad habit of talking about people "weighing" 60 kg even though we mean they weigh 600 N because we rarely need to communicate with people that have a different acceleration due to gravity. A bathroom scale reports mass in kg even though it actually measures weight. Since your mass wouldn't change on the moon, if a scale actually measured mass it would still read 60 kg. But instead it reads 1/6th that, 10 kg because the weight is 1/6th ($F=ma$, where m is unchanged but a is 1/6th that on Earth). – pentane Oct 5 '16 at 18:54

Actually, weight by definition, is the force with which the earth pulls you down. Hence, its units are Newton(since it is a force) or $kgf$(kilogram force). Now here's how to understand the difference between the two. My mass is $m$, hence my weight,W, by definition is the force with which the earth pulls me down $W=\frac{GmM}{R^2}=m\times\left(\frac{GM}{R^2}\right) =m\times g$. Here $G$ is the Universal Gravitational constant,$M$ is the mass of the earth, $R$ is the radius of the earth and $g$ is the acceleration due to gravity. So, my weight is either $mg$ Newtons or $m$ kgf. Here the acceleration due to gravity $g$ is boycotted because the comparisons of weight are usually made only on the surface of the earth, hence since the $g$ factor scales it linearly, comparisons can be made outside or without it. This local lingo of calling the weight as $m$kgf is generally called as $m$kgs. So, the weight of the man on earth is $W=60\times g = 60g = 60$kgf, whereas for a man on the moon,$W = 60\times \frac{g}{6} = 10g = 10$kgf, hence in local lingo 10kgs.