Force acting on a particle in a two dimensional XY space is given as `vec(F)=(3(Xhati+Yhatj))/((X^92)+Y^(2))^(3//2))`. Show that the force is conservative.

Force acting on a particle varies with the distance travelled by the particle as F prop(1)/((x)^(1/3)) then power due to this force varies with as:

The potential energy function of a particle in a region of space is given as U=(2xy+yz) J Here x,y and z are in metre. Find the force acting on the particle at a general point P(x,y,z).

The potential energy (in joules ) function of a particle in a region of space is given as: U=(2x^(2)+3y^(2)+2x) Here x,y and z are in metres. Find the maginitude of x compenent of force ( in newton) acting on the particle at point P ( 1m, 2m, 3m).

The position vector of a particle of mass m= 6kg is given as vec(r)=[(3t^(2)-6t) hat(i)+(-4t^(3)) hat(j)] m . Find: (i) The force (vec(F)=mvec(a)) acting on the particle. (ii) The torque (vec(tau)=vec(r)xxvec(F)) with respect to the origin, acting on the particle. (iii) The momentum (vec(p)=mvec(v)) of the particle. (iv) The angular momentum (vec(L)=vec(r)xxvec(p)) of the particle with respect to the origin.

The velocity of a particle of mass 2 kg is given by vec(v)=at hat(i)+bt^(2)hat(j) . Find the force acting on the particle.

Force acting on particle is given by vec(F) = 2xyz hat(i) + x^(2)x hat(j) + x^(2) y hat(k) . Report the amount of work done in joule in displacing a particle of mass 2 kg from (0, 0, 0) to (1, 2, 3), acted upon by the given force.

A force acting on a certain particle depends of the particles position in the xy-plane. This force F is given by the expression vec(F) = (xy hat(i) + xy hat(j)) (1 N//m^(2)) where x and y are expressed in metre. If vec(F) is a conservation force ?

Assertion: If the positon vector of a particle moving in space is given by vecr=2thati-4t^(2)hatj , then the particle moves along a parabolic trajector. Reason: vecr=xhati+yhatj and vecr=2thati-4t^(2)j rArr y=-x^(2) .

A particle is moved along the different paths OAC, OBC & ODC as shown in the figure . Path ODC is a parabola , y=4x^(2) . Find the work done by a forc vec(F)=xyhat(i)+x^(2)y on the particle along these paths. Is this force a conservative force ?