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Question

# An object of mass 2 kg is moved from infinity to a point P. Initially the object was at rest but on reaching P its speed becomes 2 m/s. If the work done in moving that object is −4 J, then find the ratio of potential energy to mass at point P (in J/kg) is

A
8
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B
8
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C
4
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D
4
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Solution

## The correct option is D −4As we know that potential energy at infinity for any object remains zero. ∴U∞=0 From question, KE∞=0 because object was at rest. Applying work-energy theorem, Wext=ΔU+ΔKE ⇒−4=Uf−Ui+KEf−KEi ⇒−4=Uf−0+12mv2−0 Given: m=2 kg; v=2 m/s ⇒Uf=−4−12×2×(2)2=−8 J ∴ potential energy per unit mass =Ufm=−82=−4 J/kg Hence, option (d) is the correct answer.

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