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  4. 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

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

Chhattisgarh PMTChhattisgarh PMT 2006

Solution:

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