Given data

• Mass of object: $m = 500\text{ g} = 0.5\text{ kg}$
• Speed as a function of position: $v = 4\sqrt{x}$

Find acceleration using $a = \frac{dv}{dt} = \frac{dv}{dx}\cdot \frac{dx}{dt} = v\frac{dv}{dx}$

Differentiate $v$ with respect to $x$ $v = 4x^{1/2}$ $\frac{dv}{dx} = 4\cdot \frac{1}{2}x^{-1/2} = \frac{2}{\sqrt{x}}$

Compute acceleration $a = v\frac{dv}{dx} = (4\sqrt{x})\left(\frac{2}{\sqrt{x}}\right) = 8\ \text{m/s}^2$

Apply Newton's second law $F = ma = 0.5 \times 8 = 4\text{ N}$

Match with options

• A: $8\text{ N}$
• B: $4\text{ N}$
• C: $5\text{ N}$
• D: $6\text{ N}$

Hence, the correct option is B.