Given data

• Mass of disc: $M = 10\,\text{kg}$
• Radius of disc: $R = 20\,\text{cm} = 0.2\,\text{m}$
• Initial angular speed: $600\,\text{rpm}$
• Final angular speed: $0$
• Time to stop: $t = 10\,\text{s}$

Convert angular speed into SI units

Since $600\,\text{rpm} = 600\times \frac{2\pi}{60}\,\text{rad/s} = 20\pi\,\text{rad/s}$

So, $\omega_0 = 20\pi\,\text{rad/s}$

Find angular deceleration

Using $\alpha = \frac{\omega - \omega_0}{t} = \frac{0 - 20\pi}{10} = -2\pi\,\text{rad/s}^2$

Retardation magnitude is $|\alpha| = 2\pi\,\text{rad/s}^2$

Moment of inertia of a solid disc about its central axis

$I = \frac{1}{2}MR^2$

Substituting values: $I = \frac{1}{2}(10)(0.2)^2 = 5\times 0.04 = 0.2\,\text{kg m}^2$

Find retarding torque

$\tau = I|\alpha|$

$\tau = 0.2 \times 2\pi = 0.4\pi\,\text{N m}$

$\tau = 4\pi \times 10^{-1}\,\text{N m}$

Match with the required format The question writes torque as: $\underline{\hspace{2cm}}\pi \times 10^{-1}\,\text{N m}$

Comparing with $4\pi \times 10^{-1}\,\text{N m}$

the required integer is: $\boxed{4}$

Comparison with stored answer

• Derived answer: $4$
• Stored correct answer: $4$
• Hence, they agree.