A particle of unit mass moves in the XY plane under the influence of a central force depending only on its distance from the origin. If (r, θ) be the polar co-ordinates of the particle at a given instant and V (r) the potential done to the given force. Then the Lagrangian for such a system is
1
\(\frac{1}{2} \dot{r}^2-V(r) \)
2
\(\frac{1}{2} m\left(\dot{r}^2+\dot{\theta}^2\right)+V(r) \)
3
\( \frac{1}{2} m\left(\dot{r}^2+r \dot{\theta}\right)+V(r) \)
4
\(\frac{1}{2} m\left(\dot{r}^2+r^2 \dot{\theta}^2\right)-V(r)\)
5
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