Question

The moon is about $ 3.8 \times {10^5}Km $ from the center of the earth. It takes about $ 27days $ for complete the orbit around the earth. Calculate the speed of the moon in Km per day.

Answer 1

Hint: Here in this question we have to find the speed of the moon in Km per day and for this, we will use the formula given by time, $ T = \dfrac{{2\pi R}}{V} $ and by substituting the values and solving it we will get the velocity for per day.

Formula used
Time to complete an orbit is given by
 $ T = \dfrac{{2\pi R}}{V} $
Here, $ T $ , will be the time,
 $ R $ , will be the radius of the moon from the earth,
 $ V $ , will be the velocity.

Complete step by step answer:
So in this question, we have the radius given by $ 3.8 \times {10^5}Km $ and the time is given as $ 27days $ . So now for calculating the time, by using the formula we will get
 $ \Rightarrow T = \dfrac{{2\pi R}}{V} $
Now on substituting the values, we will get the equation as
 $ \Rightarrow 27days = \dfrac{{2\pi \times \left( {3.8 \times {{10}^5}} \right)km}}{V} $
And from here the velocity will be given by
 $ \Rightarrow V = \dfrac{{2\pi \times \left( {3.8 \times {{10}^5}} \right)km}}{{27days}} $
As we the value of $ \pi = 3.14 $ , so on substituting the values we will get the equation as
 $ \Rightarrow V = \dfrac{{2 \times 3.14\left( {3.8 \times {{10}^5}} \right)km}}{{27days}} $
Now on solving the multiplication and division, we will get the equation as
 $ \Rightarrow V = 8.4 \times {10^4}km/days $
Therefore, the speed on the moon will be equal to $ 8.4 \times {10^4}km/days $ .

Note:
In this type of question it becomes important to memorize the formula and also by the statement of the question we have to check whether we have the diameter given or the radius given and according to the use we can take it from there. Sometimes the value of pie will be given in the question, and if it is given then we have to take that value only otherwise any one of the two.