Find the acceleration of a particle placed on the surface of the earth a

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.

Options:

A . 0.0336 m/s2

B . 4π2m/s2

C . 336 m/s2

D . none of these

Answer: Option A
:
A
Earth completes one rotation in 24 hrs
i.e. angle swept =2

π

in time=24 hrs

\Rightarrow a n g u l a r v e l o c i t y = ω = \frac{2 π}{24 \times 60 \times 60}

Centripetal acceleration =

ω^{2} R

\Rightarrow {(\frac{2 π}{24 \times 60 \times 60})}^{2} \times 6400 \times 1000

(∵ R = \frac{D i a m e t e r}{2})

\Rightarrow 0.0336 m / s^{2}

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