Binding Energy

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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).

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विखंडन प्रक्रियांमध्ये निर्माण होणाऱ्या ऊर्जेचे प्रमाण खालीलपैकी कोणत्या बाबीवर/बाबींवर अवलंबून असते ? In fission processes, the amount of energy released depends on which of the following factor/s ?

In nuclear fission processes, the energy released is directly proportional to the mass defect (loss in mass during fission, based on Einstein's E=mc^2), which is derived from the difference between reactant and product masses.

पृथ्वीभोवती वर्तुळाकार कक्षेत फिरणाऱ्या उपग्रहा $E_k$ इतकी गतिज ऊर्जा आहे. पृथ्वीच्या क्षेत्रातून बाहेर निसरण्यासाठी किमान केवढी ऊर्जा दिली पाहिजे? A satellite having circular orbit around the earth has a kinetic energy $E_k$. What is the minimum amount of energy to be added so that it escapes from the earth ?

Total energy of a satellite in a circular orbit is negative and equals -Ek. To escape to infinity, total energy must become zero, requiring an additional energy equal to its kinetic energy Ek.