InterviewSolution
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InterviewSolution
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A particle of mass m is projected from the surface of earth with a speed `V_(0)(V_(0) lt` escape velocity). Find the speed of particle at height `h = R` (radius of earth). (Take, `R = 6400 km` and `g = 9.8 m//s^(2))`A. `sqrt(gR)`B. `sqrt(v_(0)^(2)-2gR)`C. `sqrt(v_(0)^(2)-gR)`D. None of these |
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Answer» Correct Answer - C During motion of the particle, total mechanical energy remains constant. At the surface of earth, total mechanical energy is `E_(i) = (GmM)/(R) +(1)/(2)mv_(0)^(2)` `=- (GM)/(R^(2)) mR +(1)/(2)mv_(0)^(2)` `=- gmR +(1)/(2)mv_(0)^(2)` Total mechanical energy at height `h = R` is `E_(t) = (-GmM)/(2R) +(1)/(2)mv^(2)` `=- (gmR)/(2) +(1)/(2)mv^(2)` According to conservation principle of energy `E_(i) = E_(t)` `:. -gmR +(1)/(2)mv_(0)^(2) =- (gmR)/(2) +(1)/(2)mv^(2)` or `-2gR +v_(0)^(2) =- gR +v^(2)` `:. v = sqrt(v_(0)^(2)-gR)` |
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