InterviewSolution
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InterviewSolution
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A satellite of mass `m` is in a circular orbit of radius `2R_(E)` about the earth. The energy required to transfer it to a circular orbit of radius `4R_(E)` is (where `M_(E)` and `R_(E)` is the mass and radius of the earth respectively)A. `1.65 xx 10^(9)J`B. `3.13 xx 10^(9)J`C. `6.26 xx 10^(9)J`D. `4.80 xx 10^(9)J` |
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Answer» Correct Answer - B Total energy of satellite in circular orbit of radius `2R` `E_(1) = PE + KE = - (GM m)/(2R) + (1)/(2)m [sqrt((GM)/(2R))]^(2)` `= -(GM m)/(4R)` Total energy of satellite in circular orbit of radius `4R` `E_(2) = -(GM m)/(4R) + (1)/(2)m [sqrt((GM)/(4R))]^(2) = -(GM m)/(8R)` Energy spent `= E_(2) -E_(1) = -(GM m)/(8R) + (GM m)/(4R)` `=(GM m)/(8R)=(gR^(2) m)/(8R) = (mg R)/(8)` `= (400 xx 9.80 xx (6.4 xx 10^(6)))/(8) = 3.13 xx 10^(9)J` |
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