The potential energy of a body is given by U=A-Bx2 (where x is the displacement). The magnitude of force acting on the particle is

Question

The potential energy of a body is given by U=A-Bx2 (where x is the displacement). The magnitude of force acting on the particle is (A) constant (B) proportional to x (C) proportional to x2 (D) proportional to 1/x

Tardigrade Admin · Accepted Answer

Potential energy U=A-B x2 Force F=-(d U/d x) =-(0-2 Bx) F=2 B x ∴ F propto x

Q. The potential energy of a body is given by $U = A - B x^{2}$ (where x is the displacement). The magnitude of force acting on the particle is

constant

proportional to x

proportional to $x^{2}$

proportional to 1/x

Potential energy $U = A - B x^{2}$
Force $F = - \frac{d U}{d x}$
$= - (0 - 2 B x) F = 2 B x$
$∴ F \propto x$

Q. The potential energy of a body is given by U=A−Bx2 (where x is the displacement). The magnitude of force acting on the particle is