# 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

343.8k+ 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.

Recently Updated Pages

Basicity of sulphurous acid and sulphuric acid are

Define absolute refractive index of a medium

Which of the following would not be a valid reason class 11 biology CBSE

Why should electric field lines never cross each other class 12 physics CBSE

An electrostatic field line is a continuous curve That class 12 physics CBSE

What is meant by monosporic development of female class 11 biology CBSE

Trending doubts

Which country launched the first satellite in space class 11 physics CBSE

Difference Between Plant Cell and Animal Cell

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

What is the past tense of read class 10 english CBSE

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

What is pollution? How many types of pollution? Define it

Give 10 examples for herbs , shrubs , climbers , creepers

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