MPSC Rajyaseva 2020 CSAT — Question 25
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पृथ्वीच्या केंद्रापासून R इतक्या अंतरावर m इतक्या वस्तुमानाचा एका अग्निबाणाला गतिमान होण्यासाठी लागणारी ऊर्जा E = GmM_e (1/R_e - 1/R) इतकी आहे. तर ह्या अग्निबाणाला पृथ्वीच्या गुरुत्वाकर्षण क्षेत्रापासून पूर्णतः निसटण्यासाठी कमीत कमी किती वेग दिला पाहिजे ? The amount of energy needed to move a rocket having mass m from the surface of the Earth to a distance R from the Earth's center is E = GmM_e (1/R_e - 1/R). What is the minimum velocity, the rocket must have in order to completely escape the Earth's gravitational field ?
The escape velocity from the Earth's gravitational field is derived by setting the total mechanical energy to zero, yielding v = sqrt(2GMe / Re).