Question

What happens to the weight of an object when at sea level?

Answer 1

Hint: To answer our question, we will first need to understand that different people on Earth have different weights even though they have the same mass. This is due to change in height at different locations on Earth due to its diversified geography. We shall derive this equation and see what happens to the weight of an object at sea level.

Complete step-by-step solution:
 Let us initially assume that the object is at a height of ‘h’ meters above the sea level and its weight at this height is ${{W}_{h}}$. Then, this weight can be found using the expression of gravitational acceleration of Earth at different heights. This expression is given as follows:
$\Rightarrow {{g}_{h}}={{g}_{0}}{{\left( \dfrac{R}{R+h} \right)}^{2}}$
Where,
${{g}_{h}}$ is the gravitational acceleration due to Earth at a height ‘h’.
${{g}_{0}}$is the gravitational acceleration due to Earth at the sea level. And,
‘R’ is the radius of Earth.
Thus, the weight of an object at height ‘h’ will be written as:
$\Rightarrow {{W}_{h}}=m{{g}_{h}}$
$\therefore {{W}_{h}}=m{{g}_{0}}{{\left( \dfrac{R}{R+h} \right)}^{2}}$ [Let this expression be equation number (1)]
Now, the weight at the sea level can be written as:
$\Rightarrow {{W}_{s}}=m{{g}_{0}}$ [Let this expression be equation number (2)]
On comparing these two equations, we can clearly see that the weight of the object is greater when at the sea level, that is:
$\Rightarrow {{W}_{s}}\rangle {{W}_{h}}$
Hence, the weight of an object when at sea level is maximum.


Note: If one assumes that if we go further below the sea level, then our weight should increase, then it is totally wrong, as in that case, the effective mass of Earth whose gravity shall act upon us should also reduce, thus reducing the gravitational force of attraction of the Earth on us.