A particle is moving on x -axis has potential energy U=2-20 x+5 x2 Joules along x -axis. The particle is released at x=3. The maximum value of ' x . ' will be: [x is in meters and U is in joules]

Question

A particle is moving on x -axis has potential energy U=2-20 x+5 x2 Joules along x -axis. The particle is released at x=3. The maximum value of ' x . ' will be: [x is in meters and U is in joules] (A) 5 m (B) 3 m (C) 7 m (D) 8 m

Tardigrade Admin · Accepted Answer

U=2-20 x+5 x2 F=-(d U/d x)=20=10 x At equilibrium position; F=0 20-10 x=0 ⇒ x=2 Since particle is released at x=-3, therefore amplitude of particle is 5 . <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/eebe57495ccb1c84822e8e22ad530be0-.png" /> It will oscillate about x=2 with an amplitude of 5 . ∴ maximum value of x will be 7

Q. A particle is moving on x -axis has potential energy U=2−20x+5x2 Joules along x -axis. The particle is released at x=3. The maximum value of ' x. ' will be: [x is in meters and U is in joules]

5 m

3 m

7 m

8 m

U=2−20x+5x2 F=−dxdU​=20=10x At equilibrium position; F=0 20−10x=0 ⇒x=2 Since particle is released at x=−3, therefore amplitude of particle is 5 . It will oscillate about x=2 with an amplitude of 5 . ∴ maximum value of x will be 7

Q. A particle is moving on $x$ -axis has potential energy $U = 2 - 20 x + 5 x^{2}$ Joules along $x$ -axis. The particle is released at $x = 3$ . The maximum value of ' $x .$ ' will be:
$[x$ is in meters and $U$ is in joules]