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
(a) −3 J kg⁻¹
(b) −2 J kg⁻¹
(c) −5 J kg⁻⁴
(d) none of these.

Answer 1

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 V_A be the potential at point A.

$$\begin{gathered} \mathrm{Now},W=\frac{1}{2}m{v}^2+{\left(P.E.\right)}_{\mathrm{A}} \\ \Rightarrow W=\frac{1}{2}m{v}^2+V_{\mathrm{A}}\times m \\ \Rightarrow -3=\frac{1}{2}\times 1\times (2{)}^2+V_{\mathrm{A}}\times 1 \\ \Rightarrow V_{\mathrm{A}}=-5\mathrm{J}/\mathrm{Kg} \end{gathered}$$