1. Given data

• Mass of body: $m = 500\,\text{g} = 0.5\,\text{kg}$
• Velocity as a function of displacement: $v = 10\sqrt{x}$

We need to find the force acting on the body.

2. Use the relation between acceleration and velocity

When velocity is given as a function of position, acceleration is: $a = \frac{dv}{dt} = \frac{dv}{dx}\frac{dx}{dt} = v\frac{dv}{dx}$

3. Differentiate $v$ with respect to $x$

Given: $v = 10x^{1/2}$

So, $\frac{dv}{dx} = 10 \cdot \frac{1}{2}x^{-1/2} = \frac{5}{\sqrt{x}}$

4. Compute acceleration

$a = v\frac{dv}{dx} = (10\sqrt{x})\left(\frac{5}{\sqrt{x}}\right) = 50\,\text{m/s}^2$

5. Find force using Newton's second law

$F = ma = 0.5 \times 50 = 25\,\text{N}$

6. Match with options

• A: $166\,\text{N}$
• B: $5\,\text{N}$
• C: $25\,\text{N}$
• D: $125\,\text{N}$

Hence, the correct option is: $\boxed{\text{C: }25\,\text{N}}$

7. Comparison with stored correct answer

Stored correct answer: C

Our derived answer is also C, so they agree.