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| 1. |
Show the nature of the following graph for a satellite orbiting the earth. (a) KE versus orbital radius R (b) PE versus orbital radius R (b) TE versus orbital radius R |
| Answer» <html><body><p></p>Solution :`implies` consider the diagram, where a satellite of mass m, moving around the earth in a circular <a href="https://interviewquestions.tuteehub.com/tag/orbit-1138163" style="font-weight:bold;" target="_blank" title="Click to know more about ORBIT">ORBIT</a> of radius R. <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P1_C08_E04_030_S01.png" width="80%"/> <br/> Orbital speed of the satellite orbiting the earth isgiven by `V_0=sqrt((GM)/R)` <br/> where, M and R are the mass and radius of the earth.<br/> (a) ` :.`KE of a satellite of mass m, <br/>`K=1/2 mv_0^2 =1/2 mxx(GM)/R` <br/> `:. K prop 1/R` <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P1_C08_E04_030_S02.png" width="80%"/> <br/> It means the KE decreases exponentially with radius. The graph for KE versus orbital radius R is shown in figure<br/> (b) Potential energy of a satellite.<br/> P.<a href="https://interviewquestions.tuteehub.com/tag/e-444102" style="font-weight:bold;" target="_blank" title="Click to know more about E">E</a>. `=-(GMm)/R` <br/> `P.E. prop -1/R` <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P1_C08_E04_030_S03.png" width="80%"/> <br/> The graph for PE versus orbital radius R is shown in figure <br/> (c) Total energy of the satellite <br/> `E = K +U = (GMm)/(2R) - (GMm)/R` <br/> `=- (GMm)/(2R)` <br/> <img src="https://doubtnut-static.s.llnwi.net/static/physics_images/KPK_AIO_PHY_XI_P1_C08_E04_030_S04.png" width="80%"/> <br/>The graph for total energy versus orbital radius R is shown in figure <br/> <a href="https://interviewquestions.tuteehub.com/tag/note-1125278" style="font-weight:bold;" target="_blank" title="Click to know more about NOTE">NOTE</a> : We should keep in <a href="https://interviewquestions.tuteehub.com/tag/mind-1096965" style="font-weight:bold;" target="_blank" title="Click to know more about MIND">MIND</a> that Potential energy (PE) and Kinetic Energy (KE) of the satellite-earth system is always <a href="https://interviewquestions.tuteehub.com/tag/negative-570381" style="font-weight:bold;" target="_blank" title="Click to know more about NEGATIVE">NEGATIVE</a>.</body></html> | |