NEET Questions

A particle moves in a force field given by $\vec{F} = (2xy + z^3)\hat{i} + x^2\hat{j} + 3xz^2\hat{k}$. Is this force field conservative?

A particle moves in a force field described by the potential energy function $U(x, y) = \frac{1}{2}k(x^2 + y^2)$. The work done by the force field as the particle moves from (1,0) to (0,1) along a circular path centered at the origin is:

Statement- I: For a charged particle moving from point ${P}$ to point ${Q}$, the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point ${Q}$.

Statement- II: The net work done by a conservative force on an object moving along a closed loop is zero.

Assertion (A): When two unlike charges are brought nearer, their electrostatic potential energy decreases.

Reason (R) : All conservative forces act in the direction of decreasing potential energy.

It becomes possible to define potential at a point in an electric field because electric field:

If ${W_1},{W_2}\,\,{\rm{and}}\,\,{W_3}$ represent the work done in moving a particle from A to B along three different paths 1, 2, and 3 respectively, (as shown in the figure) in the gravitational field of a point mass $m$, find the correct relation between ${W_1},{W_2}\,\,{\rm{and}}\,\,{W_3}$ .

Statement-1: The angular momentum under a central force is constant.Statement-2: A force directed towards a fixed point following inverse square law is conservative

Statement-1: Work done by gravitational field in cyclic process is zeroStatement-2: Work done by conservative field does not depend upon path.

Assertion: Work done by or against gravitational force in moving a body from one point to another is independent of the actual path followed between the two points. Reason: Gravitational forces are conservative forces.

The force of gravitation is