A block is initially at rest on a smooth horizontal surface, now a variable force F=(5x−x2)i∧ N acts on the block. The value of potential energy of a block between points x=0 and x=10m, (where kinetic energy of block is 10J and block has total energy equal to its maximum potential energy)

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10.8J

12.8J

11.8J

14.8J

answer is A.

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Detailed Solution

E=∫0x(5x−x2)dx=5x22−x33 dEdx=0 for Emax 52x2-3x22=0 x=5Emax=52×(5)2−13(5)3=20.8JAt a point , K=10.0J, PE=10.8J

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