Are velocity ratio and actual mechanical advantage equal if there is no energy lose?

Yes, if there is no energy loss then velocity ratio and actual mechanical advantage are equal. Velocity ratio is the ratio of the input speed to the output speed of a machine, while actual mechanical advantage is the ratio of the output force to the input force of a machine. In an ideal scenario with no energy loss, the input force and input speed would be equal, resulting in the velocity ratio and actual mechanical advantage being equal.