Question

In the distant future, humanity has a colony on the Moon. Remember that the free-fall acceleration due to gravity on the moon is about 1/6 of what it is on Earth. Gravity on Earth= 9.8 m/s^2; Gravity on Moon= 1.6 m/s^2

a) At this time, due to inflation, bananas in a supermarket on Earth cost $50/lb. They also cost $50/lb in a supermarket on the Moon. Where will you get a better deal on bananas, or is it the same deal at both locations? In other words, if you're willing to pay $50 for a pound of bananas, which supermarket will give you more bananas in return? Explain.

b) if the price for bananas is $50/kg instead of $50/lb., where should you buy your bananas now to get the best deal, or is it the same deal in both locations? Explain.

Answer 1

mass of an object is independent of ACCELERATION DUE TO GRAVITY ( and is independent of Weight on Earth and moon).

Both pound and Kg are the unit of mass and not the Weight (which is Newton).

So in both the cases a) as well as b): it is the same deal in both locations.

weighing machines gives you weight/acceleration due to gravity. so if weighing maching is callibrated according to the acceleration due to gravity of the location, it will give same amount(mass) of bananas in both location.

Beam balance scales (old-fashioned doctor-style with the tilting beam and the sliding weight) naturally measure mass. You could move them to another planet and they'd still be accurate.