Answer:
A conservative force permits a two-way conversion between kinetic and potential energies.
The work done by a nonconservative force depends on the path taken.
A potential energy function can be specified for a conservative force.
Explanation:
A conservative force is defined as a force whose work done does not depend on the path taken, but only on the initial and final position of motion.
This means that for a conservative force, it is possible to defined a potential energy function U which depends only on the position of the object. An example of conservative force is gravity: the gravitational potential energy of an object, in fact, depends only on its position in the field, not on the path taken.
This behaviour also implies that when an object moves from A to B and then back from B to A, the potential energy gained (or lost) moving from A to B is lost (or re-gained) when moving from B to A. This means that the total mechanical energy (sum of kinetic energy and potential energy) of the object is conserved, and therefore there is a constant conversion between potential and kinetic energy during the motion.
A non-conservative force instead does not show this properties, as the work done by it depends on the path taken, and therefore it is not possible to define a potential energy function. An example of non-conservative force is friction.
According to what we wrote above, therefore, the only correct statements are:
A conservative force permits a two-way conversion between kinetic and potential energies.
The work done by a nonconservative force depends on the path taken.
A potential energy function can be specified for a conservative force.
is the buoyant force
is the density of the liquid
is the acceleration due to gravity