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Q.

A conservative force F→=(−ax+bx2)i^  is acting on a particle where a ,b are constants. The change in  potential energy when particle is displaced from  x=3m to  x=4m (Take U=0 at  x=0)

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a

37b3−7a2

b

16b−4a

c

7b−a

d

7a2−37b3

answer is D.

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Detailed Solution

∫dU=−∫F→⋅dr→∫dU=−∫34 −ax+bx2i→⋅(dxi→+dyj→+dzk→)ΔU=−∫3 −axdx+∫34 bx2dx 33ΔU=+ax2234−bx3334ΔU=7a2−37b3
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