Answer
415.2k+ views
Hint: The above numerical problem is based on the concept of the time period and rotational speed of the earth. The time period is the duration in which the earth completes the one revolution around its axis. The rotational speed varies with the time period of the earth.
Complete step by step answer:
Given: The radius of the earth is $R = 4000\;{\text{miles}}$.
The expression to calculate the rotational speed of the particle at the equator is given as:
$\omega = \dfrac{{2\pi }}{T}......\left( 1 \right)$
Here, T is the time period of the earth and its value is 24 hr.
Substitute 24 hr for T in the expression (1) to find the rotational speed of the particle on the equator.
$\omega = \dfrac{{2\pi }}{{24\;{\text{hr}}}}$
$\omega = 0.262\;{\text{rad}}/{\text{hr}}$
The expression to calculate the linear velocity of a particle on the equator is given as:
$v = R\omega ......\left( 2 \right)$
Substitute $0.262\;{\text{rad}}/{\text{hr}}$for $\omega $ in the expression (2) to calculate the linear velocity of the particle at the equator.
$v = \left( {4000\;{\text{miles}}} \right)\left( {0.262\;{\text{rad}}/{\text{hr}}} \right)$
$v = 1048\;{\text{miles}}/{\text{hr}}$
Thus, the linear velocity of the particle at the equator is $1048\;{\text{miles}}/{\text{hr}}$.
Additional Information:
The effect of the gravity on the particle varies with the location of the particle. If the particle lies on the equator of the earth then the effect of the gravity becomes minimum and becomes maximum at the poles of the earth.
Note: First calculate the time period of the earth to find the rotational speed of the particle. The units of the radius and time period should be in the same measurement system. The linear velocity of the particle varies with the distance from the surface of the earth.
Complete step by step answer:
Given: The radius of the earth is $R = 4000\;{\text{miles}}$.
The expression to calculate the rotational speed of the particle at the equator is given as:
$\omega = \dfrac{{2\pi }}{T}......\left( 1 \right)$
Here, T is the time period of the earth and its value is 24 hr.
Substitute 24 hr for T in the expression (1) to find the rotational speed of the particle on the equator.
$\omega = \dfrac{{2\pi }}{{24\;{\text{hr}}}}$
$\omega = 0.262\;{\text{rad}}/{\text{hr}}$
The expression to calculate the linear velocity of a particle on the equator is given as:
$v = R\omega ......\left( 2 \right)$
Substitute $0.262\;{\text{rad}}/{\text{hr}}$for $\omega $ in the expression (2) to calculate the linear velocity of the particle at the equator.
$v = \left( {4000\;{\text{miles}}} \right)\left( {0.262\;{\text{rad}}/{\text{hr}}} \right)$
$v = 1048\;{\text{miles}}/{\text{hr}}$
Thus, the linear velocity of the particle at the equator is $1048\;{\text{miles}}/{\text{hr}}$.
Additional Information:
The effect of the gravity on the particle varies with the location of the particle. If the particle lies on the equator of the earth then the effect of the gravity becomes minimum and becomes maximum at the poles of the earth.
Note: First calculate the time period of the earth to find the rotational speed of the particle. The units of the radius and time period should be in the same measurement system. The linear velocity of the particle varies with the distance from the surface of the earth.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)