Solve the following :


Find the acceleration of the moon with respect to the earth from the following data: Distance between the earth and the moon $=3.85 \times 10^{5} \mathrm{~km}$ and the time taken by the moon to complete one revolution around the earth $=27.3$ days.


Speed of the moon=distance/time

$=\frac{2 \pi T}{T}$

$=\frac{2 \times 3.14 \times\left(3.85 \times 10^{8}\right)}{27.3 \times 86400}$

$=1025.4 \mathrm{~m} / \mathrm{s}$

Acceleration of moon $=$

$\mathrm{A}_{\mathrm{r}}=\frac{v^{2}}{r} \frac{(1025.4)^{2}}{\left(3.85 \times 10^{8}\right)}$

$A_{r}=2.73 \times 10-3 \mathrm{~m} / \mathrm{s}^{2}$


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