The potential energy of an object of mass $m$ moving in the $xy$ plane in a conservative field is given by $U = ax + by$,where $x$ and $y$ are position coordinates of the object. Find the magnitude of its acceleration.

Assertion $(A) :-$ If work done by the force depends on the path,then the force is said to be non-conservative.
Reason $(R) :-$ All conservative forces are central forces.

$A$ body is moved along a closed loop. Is the work done in moving the body necessarily zero? If not,state the condition under which work done over a closed path is always zero.

$A$ particle moves in a potential region given by the formula $U = K(x^2 + y^2 + z^2)$. Find the force acting on the particle.

Which quantity is obtained by taking the negative derivative of potential energy with respect to displacement in the case of a conservative force?

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A$: In a central force field,the work done is independent of the path chosen.
Reason $R$: Every force encountered in mechanics does not have an associated potential energy.
In the light of the above statements,choose the most appropriate answer from the options given below: