Answer

Verified

414.6k+ 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

How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE

Why Are Noble Gases NonReactive class 11 chemistry CBSE

Let X and Y be the sets of all positive divisors of class 11 maths CBSE

Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE

Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE

Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE

Trending doubts

Establish a relation between electric current and drift class 12 physics CBSE

Guru Purnima speech in English in 100 words class 7 english CBSE

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

Difference Between Plant Cell and Animal Cell

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

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

Copper is not used as potentiometer wire because class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE