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Question
A person brings a mass of 1 kg from infinity to a point A. Initially the mass was at rest but it moves at a speed of 2 m s −1 as it reaches A. The work done by the person on the mass is −3 J. The potential at A is
Options
−3 J kg−1
−2 J kg−1
−5 J kg−4
none of these.
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Solution
−5 J kg−4
The work done by the person is equal to the kinetic energy and the potential energy of the mass of 1 kg at point A.
Let VA be the potential at point A.
\[\text { Now }, W = \frac{1}{2}m v^2 + \left( P . E . \right)_A \]
\[ \Rightarrow W = \frac{1}{2}m v^2 + V_A \times m\]
\[ \Rightarrow - 3 = \frac{1}{2} \times 1 \times (2 )^2 + V_A \times 1\]
\[ \Rightarrow V_A = - 5 J/Kg\]
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