Exams › JEE Main › Physics

Given below are two statements : Statement I: An object moves from position r1 to position r2 under a conservative force field F. The work done by the force is W = -\u222b(r1 to r2) F\u22c5dr. Statement II: Any object moving from one location to another location can follow infinite number of paths. Therefore, the amount of work done by the object changes with the path it follows for a conservative force. In the light of the above statements, choose the correct answer from the options given below :

1. (1) Both Statement I and Statement II are true
2. (2) Statement I is false but Statement II is true
3. (3) Statement I is true but Statement II is false
4. (4) Both Statement I and Statement II are false

Correct answer: (4) Both Statement I and Statement II are false

Solution

Statement I is incorrect because the work done by a conservative force is path-independent and can be calculated using the potential energy difference, not the integral of the force along the path. Statement II is also false because, while there are infinite paths between two points, the work done by a conservative force remains constant regardless of the path taken.

Related JEE Main Physics questions

• An inclined plane makes an angle \(\theta\) with the horizontal. Its top half is frictionless, while its bottom half has friction. A body released from rest at the top just reaches the bottom and comes to rest there again. The coefficient of friction on the lower half must be
• A block slides down a rough inclined plane of length $l$ and angle of inclination $\theta$. If the coefficient of friction between the block and the plane is $\mu$, what is the speed of the block when it reaches the lower end of the plane?
• A machine supplies a particle of mass $m$ with constant power $k$ watts. If the particle is initially at rest, what is the magnitude of the force acting on it at time $t$?
• A body of mass $m_1$ moving with speed $v_1$ collides head-on with another body of mass $m_2$ initially at rest. If the collision is perfectly elastic and the first body’s speed after impact becomes $\tfrac{2v_1}{3}$, what must be the ratio $m_1/m_2$?
• Two springs P and Q are alike in all respects except that their spring constants satisfy $k_P > k_Q$. They are extended first through the same extension in case (a), and then by applying the same force in case (b). If the work done by the springs is $W_P$ and $W_Q$, then the correct relation in cases (a) and (b), respectively, is
• A body is dropped from rest from a height of 10 m. If 25% of its energy is lost during collision with the ground, the greatest height it will reach after the first bounce is

⚔️ Practice JEE Main Physics free + battle 1v1 →