(a) Earth can be thought of as a sphere of radius 6400 km. Any object (or a person) is performing circular motion around the axis of earth due to earth’s rotation (period 1 day). What is acceleration of object on the surface of the earth (at equator) towards its centre ? How does these accelerations compare with g = 9.8 m/s²?

(b) Earth also moves in circular orbit around sun once every year with on orbital radius of 11 1.5 10 × m . What is the acceleration of earth (or any object on the surface of the earth) towards the centre of the sun? How does this acceleration compare with g = 9.8 m/s2?

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Answered by

Vishal Baghel | Contributor-Level 10

4 months ago

This is a Short Answer Type Question as classified in NCERT Exemplar

Explanation – a) radius of earth =6400km= 6.4 $\times 10^{6} m$

Time period = 1 day = 24 $\times 60 \times 60$ = 86400s

Centripetal acceleration a= w²r= R(2 $π / T$ )²=4 $π$ ²R/T

= $\frac{4 \times {(\frac{22}{7})}^{2} \times 6.4 \times 10^{6}}{({24 \times 60 \times 60)}^{2}}$ = 0.034m/s²

b) time = 1yr=365 $\times 24 \times 60 \times 60$ days= 365=3.15 $\times 10^{7} s$

centripetal acceleration = Rw²= $\frac{4 π^{2} R}{T^{2}}$

^{$= \frac{4 \times {\frac{22}{7}}^{2} \times 1.5 \times 10^{11}}{({3.15 \times 10^{7})}^{2}} = 5.97 \times 10^{- 3} m / s$
2}

$\frac{a_{c}}{g} = \frac{5.97 \times 10^{- 3}}{9.8} = \frac{1}{1642}$

This is a Short Answer Type Question as classified in NCERT ExemplarExplanation – a) radius of earth =6400km= 6.4 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>6</mn> </mrow> </mrow> </msup> <mi>m</mi> </math> Time period = 1 day = 24 <math> <mo>×</mo> <mn>60</mn> <mo>×</mo> <mn>60</mn> </math> = 86400sCentripetal acceleration a= w2r= R(2 <math> <mi>π</mi> <mo>/</mo> <mi>T</mi> </math> )2=4 <math> <mi>π</mi> </math> 2R/T= <math> <mfrac> <mrow> <mrow> <mn>4</mn> <mo>×</mo> <msup> <mrow> <mrow> <mfenced separators="|"> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>22</mn> </mrow> </mrow> <mrow> <mrow> <mn>7</mn> </mrow> </mrow> </mfrac> </mrow> </mrow> </mfenced> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>×</mo> <mn>6.4</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>6</mn> </mrow> </mrow> </msup> </mrow> </mrow> <mrow> <mrow> <mo>(</mo> <msup> <mrow> <mrow> <mn>24</mn> <mo>×</mo> <mn>60</mn> <mo>×</mo> <mn>60</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> </math> = 0.034m/s2b) time = 1yr=365 <math> <mo>×</mo> <mn>24</mn> <mo>×</mo> <mn>60</mn> <mo>×</mo> <mn>60</mn> </math> days= 365=3.15 <math> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>7</mn> </mrow> </mrow> </msup> <mi>s</mi> </math> centripetal acceleration = Rw2= <math> <mfrac> <mrow> <mrow> <mn>4</mn> <msup> <mrow> <mrow> <mi>π</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mi>R</mi> </mrow> </mrow> <mrow> <mrow> <msup> <mrow> <mrow> <mi>T</mi> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> </math> <math> <mo>=</mo> <mi> </mi> <mfrac> <mrow> <mrow> <mn>4</mn> <mo>×</mo> <msup> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn>22</mn> </mrow> </mrow> <mrow> <mrow> <mn>7</mn> </mrow> </mrow> </mfrac> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> <mo>×</mo> <mn>1.5</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>11</mn> <mi> </mi> </mrow> </mrow> </msup> </mrow> </mrow> <mrow> <mrow> <mo>(</mo> <msup> <mrow> <mrow> <mn>3.15</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mn>7</mn> </mrow> </mrow> </msup> <mo>)</mo> </mrow> </mrow> <mrow> <mrow> <mn>2</mn> </mrow> </mrow> </msup> </mrow> </mrow> </mfrac> <mo>=</mo> <mn>5.97</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </mrow> </msup> <mi>m</mi> <mo>/</mo> <mi>s</mi> </math> 2 <math> <mfrac> <mrow> <mrow> <msub> <mrow> <mrow> <mi>a</mi> </mrow> </mrow> <mrow> <mrow> <mi>c</mi> </mrow> </mrow> </msub> </mrow> </mrow> <mrow> <mrow> <mi>g</mi> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>5.97</mn> <mo>×</mo> <msup> <mrow> <mrow> <mn>10</mn> </mrow> </mrow> <mrow> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </mrow> </msup> </mrow> </mrow> <mrow> <mrow> <mn>9.8</mn> </mrow> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mrow> <mn>1</mn> </mrow> </mrow> <mrow> <mrow> <mn>1642</mn> </mrow> </mrow> </mfrac> </math>

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