Sign in
12thPass logo
New chatPYQ LibraryDoubtsRank report
Sign in to see Recents

Your guest activity stays on this device

Sign in to save progress →
Sign in

Work Power and Energy question

2025 · 28 Jan · Shift 1 · Q57
Guest · filters and generic practice availableBrowsing as a guest · PYQ filters and generic practice are available. Sign in only for personalised features and saved progress.
  1. PYQ Library
  2. /JEE Main
  3. /Physics
  4. /Work Power and Energy
  5. /2025 · 28 Jan · Shift 1 · Q57

Work Power and Energy question

2025 · 28 Jan · Shift 1 · Q57

JEE MainPhysicsWork Power and EnergyMCQ+4 / −1
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R\mathbf{R}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
  1. A
    A\mathbf{A}A is false but R\mathbf{R}R is true
  2. B
    Both A\mathbf{A}A and R\mathbf{R}R are true but R\mathbf{R}R is NOT the correct explanation of A\mathbf{A}A
  3. C
    A\mathbf{A}A is true but R\mathbf{R}R is false
  4. D
    Both A\mathbf{A}A and R\mathbf{R}R are true and R\mathbf{R}R is the correct explanation of A\mathbf{A}A
View written solutionFree

Correct answer: B

  1. Evaluate Assertion A

A central force has the form

F⃗=F(r) r^,\vec F = F(r)\,\hat r,F=F(r)r^,

so it depends only on the distance rrr from a fixed point and is directed along the radius vector.

Such a force is conservative, and hence there exists a potential energy function U(r)U(r)U(r) such that

F⃗=−∇U.\vec F = -\nabla U.F=−∇U.

Therefore, the work done by a central force between two points depends only on the initial and final positions, not on the path:

W=−ΔU.W = -\Delta U.W=−ΔU.

So, Assertion A is true.

  1. Evaluate Reason R

Reason R says: Every force encountered in mechanics does not have an associated potential energy.

This means that not all forces in mechanics are conservative. That is correct. For example:

  • friction,
  • viscous drag, are non-conservative forces and do not have a unique potential energy function.

So, Reason R is true.

  1. Check whether R explains A

Assertion A is about central forces being conservative, hence path-independent.

Reason R only states that not every mechanical force has potential energy. This is a general statement about forces in mechanics, but it does not explain why a central force has path-independent work.

So, both statements are true, but R is not the correct explanation of A.

  1. Choose the correct option

Thus the correct option is:

B\boxed{\text{B}}B​
  1. Comparison with stored answer

Stored correct answer: B\text{B}B

My derived answer: B\text{B}B

They match.

PreviousNext

More from Work Power and Energy

  • A body of mass 4 kg is placed on a plane at a point P having coordinate (3,4)m. Under the action of force F=(2i^+3j^​)N, it moves to a new point Q having coordinates (6,10)m…2025 · MCQ
  • In a hydraulic lift, the surface area of the input piston is 6 cm2 and that of the output piston is 1500 cm2. If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is ​…2025 · Numerical
  • A sand dropper drops sand of mass m(t) on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e., dtdm​∝v​. If P is the power delivered to run the belt at constant speed then which…2025 · MCQ
  • If a rubber ball falls from a height h and rebounds upto the height of h/2. The percentage loss of total energy of the initial system as well as velocity ball before it strikes the ground, respectively, are :2024 · MCQ
  • A body of m kg slides from rest along the curve of vertical circle from point A to B in friction less path. The velocity of the body at B is: (given, R=14 m,g=10 m/s2 and 2​=1.4) Includes diagram2024 · MCQ
  • A body of mass 50 kg is lifted to a height of 20 m from the ground in the two different ways as shown in the figures. The ratio of work done against the gravity in both the respective cases, will be : Includes diagram2024 · MCQ
  • A body is moving unidirectionally under the influence of a constant power source. Its displacement in time t is proportional to :2024 · MCQ
  • A bullet of mass 50 g is fired with a speed 100 m/s on a plywood and emerges with 40 m/s. The percentage loss of kinetic energy is :2024 · MCQ