What will be the weight of 100 kg mass on the earth surface if its volume is
compressed into the size of the moon. (mass of the earth = 6*10kg and radius
of the moon is 1.710m)?
(Ans. 1384 N)
Answers
Answer:
I think this is not that simple at all.
1 The Moon’s diameter is about 1/4 that of the Earth’s, so it’s volume is about 1/64 of Earth’s. Remember, V=4/3*pi*r^3
2 Weight and mass are not the same. My mass is about 80kg. My weight is 80kg* the_gravitational_acceleration_to_which_i_am_subject_to. About 9.81 N/kg give or take, so 80*9.81 ~ 800 N. N is the key unit, it’s newtons. Mass has little to do with gravity, aside from the fact that stuff with mass have gravity. In physics, mass refers to how hard it is to move or stop something: inertia. It is measured in kilograms. Weight on the other hand tells us how hard it is to lift that something, and this depends on both the mass of the body (a hammer for example) we are trying to lift and the mass of the body we are on (the planet). The force of gravity is G*m1*m2/(d^2) where d is the distance between the two objects and G is something we need to make the math work.
3 Since mass is exactly the same here on old-Earth and on moon-Earth, and pretty much everywhere in the universe, not much to do about it.
4 We have a problem, if we say the distance is zero, because we are on the surface... Division by zero error, programmers hate that, physicists hate that (just think/sink about black holes). But it is fairly safe to assume, for our back of a napkin math, that all the mass of the moon-Earth is a single point inside a hollow shell that is the surface. And back here on old-Earth too. So the point being in the middle, we live on a shell of glass :P
5 So the force of attraction on the old-Earth is: F1 = G*m1*m2 / radiusEarth^2, and on the moon-Earth would be F2 = G*m1*m2 / (radiusEarth/4)^2. m1 being the mass of the planet, m2 the mass of the little man.
6 G, m1 and m2 are the same, and non-zero, cause that is how the question was formulated. So we can simplify.
7 And the solution is: F2/F1 = 16. Everything would weigh 16 times more than on old-Earth, while the mass remains the same.
Now what about the little man in your question? Well, the little man’s volume does not really play here. His mass remains exactly the same. His new weight 16x his old weight.
Answer:
May be the anwer you are providng is wrong because I also came unpon this question in class 10, subject-Science , country-Nepal. If this question is in your text book then may be its answer is wrong. May be (I am also not sure) the correct answer in 1384*10^(3).
Explanation:
Mass of earth= 6*10^24 kg
mass of object = 100 kg
radius of moon (compressed earth)=1.7*10^(5)m
Now,
Weight/gravitation force = GMm/d^(2)
= [6.7*10^(-11) X 6*10^(24) X100]/(1.7*10^5)^2
=1384*10^(3)N
( If you know this question and if I am wrong, Please! suggest the right answer).