The potential energy of a particle under a conservative force is given by U(x)=(x2 - 3 x) J . The equilibrium position of the particle is at x m . The value of 10x will be

Question

The potential energy of a particle under a conservative force is given by U(x)=(x2 - 3 x) J . The equilibrium position of the particle is at x m . The value of 10x will be (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

U(x)=(x2 - 3 x)J For a conservative field, Force, F =-(d â¡ U â¡/d â¡ x) ∴ F =-(d â¡/d â¡ x)(x2 - 3 x)=-(2 x - 3)=-2x+3 At equilibrium position, F=0 -2x+3=0⇒ x=(3/2)m =1⋅ 5 textm

Q. The potential energy of a particle under a conservative force is given by $U (x) = (x^{2} - 3 x) J$ . The equilibrium position of the particle is at $x m$ . The value of $10 x$ will be

$U (x) = (x^{2} - 3 x) J$
For a conservative field, Force, $F = - \frac{d U}{d x}$
$∴ F = - \frac{d}{d x} (x^{2} - 3 x) = - (2 x - 3) = - 2 x + 3$
At equilibrium position, $F = 0$
$- 2 x + 3 = 0 \Rightarrow x = \frac{3}{2} m = 1 \cdot 5 m$

Q. The potential energy of a particle under a conservative force is given by U(x)=(x2−3x)J . The equilibrium position of the particle is at xm . The value of 10x will be

U(x)=(x2−3x)J For a conservative field, Force, F=−d⁡xd⁡U⁡​ ∴F=−d⁡xd⁡​(x2−3x)=−(2x−3)=−2x+3 At equilibrium position, F=0 −2x+3=0⇒x=23​m=1⋅5m

Q. The potential energy of a particle under a conservative force is given by $U (x) = (x^{2} - 3 x) J$ . The equilibrium position of the particle is at $x m$ . The value of $10 x$ will be

$U (x) = (x^{2} - 3 x) J$
For a conservative field, Force, $F = - \frac{d U}{d x}$
$∴ F = - \frac{d}{d x} (x^{2} - 3 x) = - (2 x - 3) = - 2 x + 3$
At equilibrium position, $F = 0$
$- 2 x + 3 = 0 \Rightarrow x = \frac{3}{2} m = 1 \cdot 5 m$