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Let \( r \) be the distance of a particle from a fixed point to which it is attracted by an inverse square law force given by \( F=k / r^{2} \quad(k= \) constant \( ) \). Let \( m \) be the mass of the particle and \( L \) be its angular momentum with respect to the fixed point. Which of the following formulae is correct about the total energy of the system?
(1) \( \frac{1}{2} m\left(\frac{d r}{d t}\right)^{2}-\frac{k}{r}+\frac{L}{2 m r^{2}}= \) Constant
(2) \( \frac{1}{2} m\left(\frac{d r}{d t}\right)^{2}-\frac{k}{r}= \) Constant
(3) \( \frac{1}{2} m\left(\frac{d r}{d t}\right)^{2}+\frac{k}{r}+\frac{L^{2}}{2 m r^{2}}= \) Constant
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