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Which of the following statements about conservation laws for a particle moving in one dimension under the influence of a potential V(x) is true?
  • a)
    The total energy of the system is conserved if the potential V(x) is an even function of x.
  • b)
    The total momentum of the system is conserved if the potential V(x) is an odd function of x.
  • c)
    The total angular momentum of the system is conserved if the potential V(x) is spherically symmetric.
  • d)
    The total energy of the system is conserved if the potential V(x) is time independent.
Correct answer is option 'D'. Can you explain this answer?
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Which of the following statements about conservation laws for a partic...
Concept:
Conservation laws are fundamental principles in physics that describe quantities that remain constant over time, even as other aspects of the system may change.
There are several types of conservation laws, including conservation of energy, momentum, angular momentum, and charge.
Conservation of energy states that the total amount of energy in a closed system is constant over time.
Conservation of momentum states that the total momentum of a system remains constant if there are no external forces acting on the system.
Conservation of angular momentum states that the total angular momentum of a system remains constant if there are no external torques acting on the system. 
Conservation of charge states that the total electric charge of a closed system is constant over time. 
Overall, conservation laws are important because they provide fundamental constraints on physical systems and help us understand how energy, momentum, angular momentum,
and charge are conserved and transformed in different contexts.
Explanation:
Conservation laws are fundamental principles in physics that describe quantities that are conserved over time.
For a particle moving in one dimension, the total energy of the system is given by E = (1/2)mv^2 + V(x), where m is the mass of the particle, v is its velocity, and V(x) is the potential energy.
The total energy of the system is conserved if and only if the potential V(x) is time-independent, so option (4) is correct.
Option (1) is incorrect because the potential being even or odd doesn't necessarily imply energy conservation.
Option (2) is incorrect because momentum conservation depends on the absence of external forces acting on the particle, not the parity of the potential.
Option (3) is incorrect because the concept of angular momentum only applies in three dimensions when the potential is spherically symmetric.
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Directions: Read the given passage carefully and answer the following question:Heritage conservation practices improved worldwide after the International Centre for the Study of the Preservation and Restoration of Cultural Property (ICCROM) was established with UNESCO’s assistance in 1959. The inter-governmental organisation with 126 member states has done a commendable job by training more than 4,000 professionals, providing practice standards, and sharing technical expertise. In this golden jubilee year, as we acknowledge its key role in global conservation, an assessment of international practices would be meaningful to the Indian conservation movement. Consistent investment, rigorous attention, and dedicated research and dissemination are some of the positive lessons to imbibe. Countries such as Italy have demonstrated that prioritising heritage with significant budget provision pays. On the other hand, India, which is no less endowed in terms of cultural capital, has a long way to go. Surveys indicate that in addition to the 6,600 protected monuments, there are over 60,000 equally valuable heritage structures that await attention. Besides the small group in the service of Archaeological Survey of India, there are only about 150 trained conservation professionals. In order to overcome this severe shortage, the emphasis has been on setting up dedicated labs and training institutions. It would make much better sense for conservation to be made part of mainstream research and engineering institutes, as has been done in Europe.Increasing funding and building institutions are the relatively easy part. The real challenge is to redefine international approaches to address local contexts. Conservation cannot limit itself to enhancing the art-historical value of the heritage structures, which international charters perhaps overemphasise. The effort has to be broad-based: It must also serve as a means to improving the quality of life in the area where the heritage structures are located. The first task, therefore, is to integrate conservation efforts with sound development plans that take care of people living in the heritage vicinity. Unlike in western countries, many traditional building crafts survive in India, and conservation practices offer an avenue to support them. This has been acknowledged by the Indian National Trust for Art and Cultural Heritage charter for conservation but is yet to receive substantial state support. More strength for heritage conservation can be mobilised by aligning it with the green building movement. Heritage structures are essentially eco-friendly and conservation could become a vital part of the sustainable building practices campaign in future.Q.Which of the following statements best describe(s) the major challenge faced in the implementation of international conservation policies?

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Which of the following statements about conservation laws for a particle moving in one dimension under the influence of a potential V(x) is true?a)The total energy of the system is conserved if the potential V(x) is an even function of x.b)The total momentum of the system is conserved if the potential V(x) is an odd function of x.c)The total angular momentum of the system is conserved if the potential V(x) is spherically symmetric.d)The total energy of the system is conserved if the potential V(x) is time independent.Correct answer is option 'D'. Can you explain this answer?
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Which of the following statements about conservation laws for a particle moving in one dimension under the influence of a potential V(x) is true?a)The total energy of the system is conserved if the potential V(x) is an even function of x.b)The total momentum of the system is conserved if the potential V(x) is an odd function of x.c)The total angular momentum of the system is conserved if the potential V(x) is spherically symmetric.d)The total energy of the system is conserved if the potential V(x) is time independent.Correct answer is option 'D'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about Which of the following statements about conservation laws for a particle moving in one dimension under the influence of a potential V(x) is true?a)The total energy of the system is conserved if the potential V(x) is an even function of x.b)The total momentum of the system is conserved if the potential V(x) is an odd function of x.c)The total angular momentum of the system is conserved if the potential V(x) is spherically symmetric.d)The total energy of the system is conserved if the potential V(x) is time independent.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following statements about conservation laws for a particle moving in one dimension under the influence of a potential V(x) is true?a)The total energy of the system is conserved if the potential V(x) is an even function of x.b)The total momentum of the system is conserved if the potential V(x) is an odd function of x.c)The total angular momentum of the system is conserved if the potential V(x) is spherically symmetric.d)The total energy of the system is conserved if the potential V(x) is time independent.Correct answer is option 'D'. Can you explain this answer?.
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