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Electricity
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answer is 2)
the reason is the correct explanation as 2) is the defining statement of a conservative force
1) is true because of 2)
and 1) can be proved mathematically using 2)...
ie a force cannot be conservative if 2) isnt true and 1) can be true even if 2) isnt for a non conservative force,
im sure u must have come across
the example given in IE Irodov
consider a rough track of arbitrary shape
such as shown below...
the work done by friction in taking a body of mass m from A to B is -umgd u is the coefficient of friction
this can be proved by integration
clearly it is independent of path and depends only on horizontal separation between A to B
independent of path bet A n B(shape of curve)
but friction is not conservative as
the work done in a closed loop is not zero
see, work done in taking the body from B to A is also -umgd...
so net work done in taking m to B and bringing back it to A (work done by friction) is -2umgd
although it is independent of path between A and B (work is -2umgd irrespective of the shape of path bet. A n B)
but work done in closed loop isnt zero so friction isnt a conservative force.
2) is the defining statement of conservative force.. and it can be mathematically proved that 1) is true because 2) is.,,












