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

The correct option is Proportional to x.

To understand why this is correct, we need to look at the relationship between the potential energy of a particle and the conservative force acting on it.

In physics, the conservative force $F$ acting on a particle in one dimension is defined as the negative gradient (or negative derivative with respect to position) of its potential energy $U$:

$$F=-\frac{dU}{dx}$$

Here, the potential energy is given as:

$$U=B{x}^2$$

where $B$ is a constant and $x$ is the displacement.

Now, we calculate the derivative of potential energy with respect to $x$:

$$\frac{dU}{dx}=\frac{d}{dx}\left(B{x}^2\right)=2Bx$$

Substituting this derivative back into the force equation gives:

$$F=-2Bx$$

The question asks for the magnitude of the force, which is the absolute value of $F$:

$$\left|F\right|=2\left|B\right|x$$

Since $2\left|B\right|$ is a constant, the magnitude of the force is directly proportional to the displacement $x$:

$$\left|F\right|\propto x$$