Question

An object is weighed in the following places using a spring balance. In which place will it weigh the heaviest?

1. On the Moon
2. At the equator
3. At the pole
4. In outer space

Answer 1

Here we need to consider each option carefully, calculate the force of gravity for each case and compare the distance and gravitational constant. Here the gravitational force would be equal to the mass times acceleration where acceleration is the acceleration due to gravity g, so the force will become the weight of the object. F = ma, where F = force, m = mass, a = acceleration. It will become W = mg, W = force exerted by gravity, m = mass of the object, g = acceleration due to gravity g.

Formula used:
$F = G\dfrac{{Mm}}{{{r^2}}}$;
Where:
F = force;
m = mass of object 1;
M = Mass of object 2;
a = acceleration;
G = Gravitational Constant.
r = Distance;

Complete step-by-step answer:
Step 1: Compare the force of gravity on the moon to the force of gravity on earth.
${F_m} = G\dfrac{{{M_m}{m_0}}}{{{r^2}}}$; …(${M_m}$= Mass of moon; ${m_0}$= Mass of object)
${F_e} = G\dfrac{{{M_e}{m_0}}}{{{r^2}}}$; …(${M_e}$= Mass of earth;${m_0}$= Mass of object)
Here we know that the mass of moon is less than the mass of earth so,
${F_m} < {F_e}$;
Option “1” is ruled out.
Step 2: Compare the force of gravity at equator to the force of gravity at poles.
Force of gravity at equator:
${F_{eq}} = G\dfrac{{Mm}}{{{r_e}^2}}$; …(${r_e}$= distance from the equator to the object).
${F_{po}} = G\dfrac{{Mm}}{{{r_p}^2}}$; …(${r_p}$= distance from the pole to the object).
We know that the distance from the equator to the object is greater than the distance from the pole to the object:
${r_e}$>${r_p}$;
We can infer from that the force of gravity at the equator is less than the force of gravity at poles.
${F_{eq}}$< ${F_{po}}$;
Option “2” is ruled out.
Step 3: Here we know that there is no gravity in outer space. So, there would be no weight or zero weight of the object.
Hence Option “4” is ruled out.
Step 4: Now, only option “3” is left out. From the gravitational force formula we know that the gravitational force is maximum at the poles. This is because at the pole the distance between the earth’s core and the earth's surface is minimum.

Final Answer: Option “3” is correct. An object is weighed using a spring balance would be the heaviest at the poles of the earth.

Note: Here one needs to explain each and every option as to why the particular option is incorrect. So, go step by step and carefully compare the mass, the distance and the force of gravity of each option mentioned.