The potential energy function of a particle in a region of space is given as: U=(2 x2 + 3 y3 + 2 z)J Here x,y and z are in meters. Find the force acting on the particle at point P(.1m,2m,3m.):-

Question

The potential energy function of a particle in a region of space is given as: U=(2 x2 + 3 y3 + 2 z)J Here x,y and z are in meters. Find the force acting on the particle at point P(.1m,2m,3m.):- (A) -(.4 hati+36 hatj+2 hatk.)N (B) -4 hati+36 hatj+9 hatk (C) -8 hati-18 hatj+2 hatk (D) -4 hati+18 hatj-9 hatk

Tardigrade Admin · Accepted Answer

U2=(2 x2 + 3 y3 + 2 z) ⇒ overset arrow F=-(( partial U/ partial x) hati + ( partial U/ partial y) hatj + ( partial U/ partial z) hatk) =-(4 xi + 9 y2 hatj + 2 hatk)N so, ( overset arrow F)(. 1 , 2 , 3 .)=-(.4 hati+36 hatj+2 hatk.)N

Q. The potential energy function of a particle in a region of space is given as :
$U = (2 x^{2} + 3 y^{3} + 2 z) J$
Here $x, y$ and $z$ are in meters. Find the force acting on the particle at point $P (1 m, 2 m, 3 m) : -$

$- (4 \hat{i} + 36 \hat{j} + 2 \hat{k}) N$

$- 4 \hat{i} + 36 \hat{j} + 9 \hat{k}$

$- 8 \hat{i} - 18 \hat{j} + 2 \hat{k}$

$- 4 \hat{i} + 18 \hat{j} - 9 \hat{k}$

$U_{2} = (2 x^{2} + 3 y^{3} + 2 z)$
$\Rightarrow F \to = - (\frac{\partial U}{\partial x} \hat{i} + \frac{\partial U}{\partial y} \hat{j} + \frac{\partial U}{\partial z} \hat{k})$
$= - (4 x i + 9 y^{2} \hat{j} + 2 \hat{k}) N$
so, $(F \to)_{(1, 2, 3)} = - (4 \hat{i} + 36 \hat{j} + 2 \hat{k}) N$

Q. The potential energy function of a particle in a region of space is given as : U=(2x2+3y3+2z)J Here x,y and z are in meters. Find the force acting on the particle at point P(1m,2m,3m):−

−(4i^+36j^​+2k^)N

−4i^+36j^​+9k^

−8i^−18j^​+2k^

−4i^+18j^​−9k^