Question

Rahul buys 100 g of silver at the north pole and hands it over to his friend at the equator. Now the weight found by his friend will be ___________________ the weight of silver bought.
A) greater than
B) less than
C) same as
D) cannot be determined.

Answer 1

Hint: Weight of any object is defined as the product of the mass of the object and the acceleration due to gravity at the place at which the weight is measured. The acceleration due to gravity at the equator is less than the acceleration due to gravity at the north pole.

Formula Used:
Weight of an object is given by, $W = mg$ where $m$ is the mass of the object and $g$ is the acceleration due to gravity at the place of measurement.

Complete step by step answer:
Step 1: Describe the weight of the silver at the equator.
The weight of the silver bought by Rahul at the north pole is given as 100 g. This 100 g of silver is then handed over to his friend at the equator.
Weight of the silver at the pole can be expressed as ${W_p} = m{g_p} = 100{\text{g}}$ where $m$ is the mass of the object and ${g_p}$ is the acceleration due to gravity at the north pole.
Then the weight of the silver at the equator can be expressed as ${W_e} = m{g_e}$ where $m$ is the mass of the object and ${g_e}$ is the acceleration due to gravity at the equator.
The acceleration due to gravity at the equator is less than that at the north pole, i.e., ${g_e} < {g_p}$.
This is because, at the equator, the centrifugal force which arises due to the Earth’s spinning is maximum and is minimum at the pole.
Hence, we find that ${W_e} < {W_p}$.
Thus Rahul’s friend will find the weight of silver he received to be less than the weight of the silver bought.
So the correct option is B.

Note: The less acceleration due to gravity at the equator can also be explained based on the radius of the Earth. The radius of the equator, i.e. the distance from the centre of the Earth to the equator is more than the radius of the pole. The acceleration due to gravity $g$ is inversely proportional to the radius and so it will be less at the equator.