A body rotating with an angular speed of 600 rpm is uniformly accelerated to 1800 rpm in 10 sec. The number of rotations made in the process is ___.

The initial angular speed is $$\omega_1 = 600 \text{ rpm}$$ and the final angular speed is $$\omega_2 = 1800 \text{ rpm}$$. The time taken is $$t = 10$$ s.

The average angular speed during uniform acceleration is:

$$\omega_{\text{avg}} = \frac{\omega_1 + \omega_2}{2} = \frac{600 + 1800}{2} = 1200 \text{ rpm}$$

The total number of rotations is:

$$N = \omega_{\text{avg}} \times t = 1200 \text{ rpm} \times \frac{10}{60} \text{ min} = 1200 \times \frac{1}{6} = 200 \text{ rotations}$$