Question

The value of acceleration due to gravity is $980\,cm{s^{ - 2}}$. What will be its value if the unit of length is kilometre and that time is minute?

Answer 1

Let us first get some idea about the acceleration due to gravity. The acceleration gained by an object due to gravitational force is known as acceleration owing to gravity. The SI unit for it is $m \times {s^{ - 2}}$.It is a vector quantity since it has both magnitude and direction. The acceleration owing to gravity is denoted by the letter$g$. $g$ has a standard value of $9.8{\text{ }}m{s^{ - 2}}$ on the earth's surface at sea level.

Complete step-by-step solution:
As given in the problem:
$g = 980\,cm{s^{ - 2}}$
As we know that:
$1\,cm = \dfrac{1}{{{{10}^5}}}km$ and $1s = \dfrac{1}{{60}}\min$
Now, if we substitute the above value in the g then we will get:
$g = 980 \times {10^{ - 5}} \times 60 \times 60\,km/{\min ^2}$
$g = 35.28\,km/{\min ^2}$

Additional Information:
Variation of $g$ due to shape of Earth:
The earth's radius at the equator is greater than its radius at the poles because it is an oblate spheroid. Because the acceleration due to gravity for a source mass is inversely proportional to the square of the earth's radius, it varies with latitude due to the earth's shape.
$\dfrac{{{g_p}}}{{{g_e}}} = \dfrac{{R_e^2}}{{R_p^2}}$
Where ${g_e}$ and${g_p}$ are the gravitational accelerations at the equator and poles, respectively, and ${R_e}$and ${R_p}$are the earth's radii near the equator and poles. It is obvious from the preceding equation that gravity accelerates more near the poles and less in the equator. As the value of g drops, a person's weight falls as he moves from the equator to the poles.

Note: In order to solve this problem there are some important points which we should keep in our fingertips. Unit conversion is the most important point to solve this problem. These are the some conversion we should keep in our mind:
$10\,mil\lim eters\,(mm) = 1\,centimeter\,(cm)$
$10\,centimeters = 1\,decimeter\,(dm) = 100\,mil\lim eters$
$100\,centimeter = 1\,meter(m) = 1000\,mil\lim eters$
$1000\,meters = 1\,kilometer\,(km)$.