According to the principle of conservation of mechanical energy, the decrease in potential energy is equal to the increase in kinetic energy when objects fall along frictionless paths . If an object falls from a vertical height $h$, then: $mgh = \frac{1}{2}mv^2$ $v = \sqrt{2gh}$ This expression shows that the final speed $v$ on reaching the ground depends only on the vertical height $h$ and the acceleration due to gravity $g$, and is completely independent of the mass of the object or the shape of the path taken (as long as it is frictionless). Since all three objects fall from the same point 'O', they have the same vertical displacement $h$. Therefore, they will all reach the ground with the same speed. The ratio of their speeds will be $1 : 1 : 1$.