(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?

2 Views | Posted 4 months ago

Asked by Shiksha User

1 Answer

Answered by

alok kumar singh | Contributor-Level 10

4 months ago

This is a Short Answer Type Questions 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 Questions 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>

0 Upvotes 0 Downvotes

1 Answer

Similar Questions for you

Learn more about...

Most viewed information

Most viewed information

Share Your College Life Experience

Didn't find the answer you were looking for?

Need guidance on career and education? Ask our experts

Your Question