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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

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Solution

The correct option is **D** −4

As 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.

As 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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