Question

Find the acceleration of a particle placed on the surface of the earth at the equator due to earth's rotation. The diameter of earth = 12800 km and it takes 24 hours for the earth to complete one revolution about its axis.

Answer 1

Diameter of the Earth = 12800 km
So, radius of the Earth, R = 6400 km = 6.4 × 10⁶ m

Time period of revolution of the Earth about its axis:

$$\begin{gathered} T=24\mathrm{hr}=24\times 3600\mathrm{s} \\ v=\frac{2\mathrm{\pi }r}{T}=\frac{2\times 3.14\times 64\times {10}^6}{24\times 3600} \end{gathered}$$
^{$\Rightarrow v=465.185\mathrm{m}/\mathrm{s}$}
$$\begin{gathered} \mathrm{Acceleration}\mathrm{of}\mathrm{the}\mathrm{particle}: \\ \mathrm{a}=\frac{v^{\mathit{2}}}{R}=\frac{{\left(465.185\right)}^2}{64\times {10}^5}=0.038\mathrm{m}/{\mathrm{s}}^2 \end{gathered}$$