The potential energy function for a two dimensional fore is `U=+2x^(3)-4x^(2)y+6y^(2)` where `U` is in joules `x` and `y` are in meters. The force (in `N`) acting on particle is `(3,2)` is `Ahati+Bhatj` Find `A+B`.

The potential energy of a particle oscillating along x-axis is given as U=20+(x-2)^(2) Here, U is in joules and x in meters. Total mechanical energy of the particle is 36J . (a) State whether the motion of the particle is simple harmonic or not. (b) Find the mean position. (c) Find the maximum kinetic energy of the particle.

The potential energy (in joules ) function of a particle in a region of space is given as: U=(2x^(2)+3y^(2)+2z) 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 potential energy (U) of a body of unit mass moving in a one-dimension force field is given by U=(x^(2)-4x+3) . All units are in S.L

The potential energy of a particle of mass 1 kg moving in X-Y plane is given by U=(12x+5y) joules, where x an y are in meters. If the particle is initially at rest at origin, then select incorrect alternative :-

The potential energy of a system under the influence of conservative force at position x is V(x) =[3x^(2)+4x+5] .At x = 2 m the conservative force acting on the system is ……….

The potential energy of a particle varies with distance x from a fixed origin as U = (A sqrt(x))/( x^(2) + B) , where A and B are dimensional constants , then find the dimensional formula for AB .

The potential energy for a force filed vecF is given by U(x,y)=cos(x+y) . The force acting on a particle at position given by coordinates (0, pi//4) is

The potential energy of 1 kg particle , free to move allong is given by U(x) = ((x^(3))/3-(x^(2))/2) I . if its mechanical energy is 2J . Its maximum speed is …… ms^(-1)

Differentiate the following functions with respect to x: x^(2) + y^(2) - 4x- 6y - 25= 0