1. Given data

• Moment of inertia: $I = 0.40\,\mathrm{kg\,m^2}$
• Radius of wheel: $r = 10\,\mathrm{cm} = 0.10\,\mathrm{m}$
• Pulling force: $F = 40\,\mathrm{N}$
• Initial angular velocity: $\omega_0 = 0$
• Time: $t = 10\,\mathrm{s}$

2. Find the torque on the wheel

The force is applied tangentially through the string, so torque is

$\tau = F r$

$\tau = 40 \times 0.10 = 4\,\mathrm{N\,m}$

3. Find angular acceleration

Using rotational form of Newton's second law,

$\tau = I\alpha$

So,

$\alpha = \frac{\tau}{I} = \frac{4}{0.40} = 10\,\mathrm{rad/s^2}$

4. Find angular velocity after 10 s

Using

$\omega = \omega_0 + \alpha t$

$\omega = 0 + 10 \times 10 = 100\,\mathrm{rad/s}$

5. Final answer

$x = 100$

The derived answer matches the stored correct answer.