how will the gravitational potential energy of a book shelf fixed on a wall be affected when more number of books are placed in it?
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The gravitational potential energy will increase as the mass on it will increase.
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As mass is one of the factors for gravitational potential energy, the number of books effectively increases the mass of the bookshelf, thereby increasing its potential energy. Supposing the floor gave way, would a loaded bookshelf reach the ground faster (due to greater kinetic energy) or an empty one? It's the one with more books. Ergo, the gravitational potential energy is increased by placing more books in it.
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