Conservative Forces — Prelims Questions

Which of the following forces is NOT a conservative force?

A particle moves from point A to point B under the influence of a conservative force. The potential energy at A is $10,\text{J}$ and at B is $30,\text{J}$. What is the work done by the conservative force?

The potential energy of a particle in a force field is given by $U(x) = 5x^2 - 4x + 2,\text{J}$. The magnitude of the force acting on the particle at $x = 2,\text{m}$ is:

A block of mass $m = 1,\text{kg}$ is released from rest at the top of a frictionless incline of height $h = 5,\text{m}$. Using the principle of conservation of mechanical energy, what is the speed of the block when it reaches the bottom of the incline? (Take $g = 10,\text{m/s}^2$)

Which of the following statements is TRUE regarding a conservative force?

A particle is subjected to a force $vec{F} = (3x^2hat{i} + 2yhat{j}),\text{N}$. Is this force conservative?