Question

Why is acceleration constant in free fall?

Answer 1

Free fall: When the only force acting on the object is gravity due to earth, then the object is said to be in the state of free fall.

1. When an object falls freely toward the earth's surface, the only force acting on the object is gravity $\left(\mathrm{g}\right)$.
2. From the equation of gravity we have $\mathrm{g}=\frac{\mathrm{GM}}{{\mathrm{r}}^2}$; where $\mathrm{G}$ is gravitational constant, $\mathrm{M}$ is mass of earth and $\mathrm{r}$ is the earth's radius.
3. Since the object is falling toward the earth, from the equation, we can say that the mass $\left(\mathrm{M}\right)$ and radius $\left(\mathrm{r}\right)$ of the earth remain constant.
4. Let $h$be the height of the object during free fall at any instant and $h<<r$.
5. Then the equation of gravity becomes $g=\frac{GM}{{\left(r+h\right)}^2}$ ; where $\mathrm{G}$ is gravitational constant, $\mathrm{M}$ is mass of earth, $h$ is equal to height of falling object and $\mathrm{r}$ is the earth's radius.
6. So, the equation of $\mathrm{g}$ will remain constant throughout.

Thus, acceleration is constant in free fall.