# Calculate the change in the value of g at angle of 45 degree. Take radius of earth $ = 6.37 \times {10^3}km$

A) $ - 0.064m/{s^2}$

B) $ - 0.0168m/{s^2}$

C) $ - 0.023m/{s^2}$

D) $ - 0.0548m/{s^2}$

Answer

Verified

290.7k+ views

**Hint:**The basic approach to solve this question is by applying the formula of variation of acceleration due to gravity with angle made horizontally with the earth. The formula is given below

$\Delta g = g' - g = - R{\omega ^2}{\cos ^2}\theta $

Where g’ is the new acceleration due to gravity at an angle of $\theta $

g is the acceleration due to gravity on the surface of earth whose formula is $\dfrac{{GM}}{{{R^2}}}$

R is the radius of earth

$\omega $ is the angular frequency

$\theta $ is the angle with the horizontal axis of earth or with equator

**Complete step by step answer:**

According to the question the given quantities are

$R = 6.37 \times {10^3}km$ Where $R$ is the radius

$\theta = {45^o}$ $\theta $ is the angle with the horizontal axis of earth or with equator

Now to calculate angular frequency,

In one day we have 24 hours that is $24 \times 60 \times 60$ seconds

Now $w = \dfrac{{2\pi }}{T}$ where T is the time period which is total seconds in a day and $\omega $ is the angular frequency mentioned also.

Hence $w = \dfrac{{2\pi }}{{24 \times 3600}} = 7.2 \times {10^{ - 5}}rad\,{s^{ - 1}}$

Now let us recall the that we have discussed earlier

$\Delta g = - R{\omega ^2}{\cos ^2}\theta $

Putting the values given,

$\Delta g = - (6.37 \times {10^6}){(7.2 \times {10^{ - 5}})^2}{\cos ^2}45$

On simplifying further, we get,

$\Delta g = 1.65 \times {10^{ - 2}}$

Which is the required answer, therefore the correct option is B) $ - 0.0168m/{s^2}$

**Note:**We also have different regarding depth and altitude

For depth $g' = g\left( {1 - \dfrac{d}{R}} \right)$ where d is the depth. The formula

For altitude $g' = g\left( {1 - \dfrac{{2h}}{R}} \right)$ where h is the altitude.

For both the equations above R and G are constant. Both the above formula comes from a assumption or a proof in Binomial theorem in Mathematics which say

For ${(1 + x)^n}$ if, ${x^2}$ and the further terms are very small then, this expression can be assumed as $1 + nx$. Now in both the equations above whether of altitude or of depth $\dfrac{d}{R}$ and $\dfrac{{2h}}{R}$ have squares, cubes and further powers are very small hence, can be neglected.

Last updated date: 04th Jun 2023

•

Total views: 290.7k

•

Views today: 7.46k

Recently Updated Pages

Which element possesses the biggest atomic radii A class 11 chemistry JEE_Main

The highly efficient method of obtaining beryllium class 11 chemistry JEE_Main

Which of the following sulphates has the highest solubility class 11 chemistry JEE_Main

Amongst the metal Be Mg Ca and Sr of group 2 of the class 11 chemistry JEE_Main

Which of the following metals is present in the greencolored class 11 chemistry JEE_Main

To prevent magnesium from oxidation in the electrolytic class 11 chemistry JEE_Main

Trending doubts

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Change the following sentences into negative and interrogative class 10 english CBSE

A Short Paragraph on our Country India

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

What is the difference between anaerobic aerobic respiration class 10 biology CBSE