Which of the given statements are correct for a conservative force field(p) The total mechanical energy is conserved.(q) The work done around a closed path is zero.(r) Gain in kinetic energy = Loss in potential energy.a)(p) andamp; (q)b)Only (p)c)(p), (q) andamp; (r)d)(q) andamp; (r)Correct answer is option 'C'. Can you explain this answer?

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Which of the given statements are correct for a conservative force field

(p) The total mechanical energy is conserved.
(q) The work done around a closed path is zero.
(r) Gain in kinetic energy = Loss in potential energy.

a)
(p) & (q)
b)
Only (p)
c)
(p), (q) & (r)
d)
(q) & (r)

Correct answer is option 'C'. Can you explain this answer?

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Which of the given statements are correct for a conservative force fie...

CONCEPT:

Conservative force: A force is conservative if the work done by the force in displacing an object from one point to another point is independent of the path followed by the object and depends only on the endpoints.
Electrostatic forces, gravitational forces, elastic forces, magnetic forces, etc and are examples of conservative forces.

Non-conservative forces: A force is said to be non-conservative if work done by or against the force in moving a body from one position to another, depends on the path followed between these two positions.
Examples: Frictional force, Viscous force, Airdrag, etc.

EXPLANATION:

Suppose a particle starts at A and a force F_ext is acting on it. The particle is moved around the loop using the same force, F_ext
Suppose the particle eventually ends up at A itself then the entire displacement of the particle is zero which means the total work done is zero.
A total work of one zero means there is no expenditure of energy which means the total energy is conserved. Hence statement p is correct
The total displacement of a particle in a closed loop is zero, which means the total work done is zero. Hence statement q is correct.
The total mechanical energy of a system is given by

⇒ Total energy = Potential Energy + Kinetic energy

From the statement p, it is clear that if the total work done is zero it means the energy is conserved.
Which means Gain in kinetic energy = Loss in Potential Energy. Hence option r is correct.

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Which of the given statements are correct for a conservative force fie...

True, (q) False, (r) True

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Which of the given statements are correct for a conservative force field(p) The total mechanical energy is conserved.(q) The work done around a closed path is zero.(r) Gain in kinetic energy = Loss in potential energy.a)(p) & (q)b)Only (p)c)(p), (q) & (r)d)(q) & (r)Correct answer is option 'C'. Can you explain this answer?

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