Integer Type Numericals for JEE (Advanced):

1. Centripetal acceleration: $$a_c = \frac{v^2}{r}=\frac{(10 \ m/s)^2}{5 \ m} = 20 \ m/s^2$$

2. Centripetal acceleration: $$a_c = \frac{v^2}{r}=\frac{(36 \ km/h)^2}{(100 \ m)} = 12.96 \ m/s^2$$

3. Angular velocity: $$\omega = \frac{2\pi}{T}=\frac{2\pi \ rad}{5 \ s} = 1.257 \ rad/s$$

4. Linear speed: $$v = r\omega = (10 \ m)(2 \ rad/s) = 20 \ m/s$$

5. Angular velocity: $$\omega = \frac{2\pi N}{60}=\frac{2\pi (600 \ rpm)}{60} = 62.83 \ rad/s$$

Integer Type Numericals for JEE (Main):

1. Centripetal acceleration: $$a_c = \frac{v^2}{r}=\frac{(5 \ m/s)^2}{2 \ m} = 12.5 \ m/s^2$$

2. Centripetal acceleration: $$a_c = \frac{v^2}{r}=\frac{(18 \ km/h)^2}{(50 \ m)} = 6.48 \ m/s^2$$

3. Angular velocity: $$\omega = \frac{2\pi}{T}=\frac{2\pi \ rad}{10 \ s} = 0.628 \ rad/s$$

4. Linear speed: $$v = r\omega = (5 \ m)(1 \ rad/s) = 5 \ m/s$$

5. Angular velocity: $$\omega = \frac{2\pi N}{60}=\frac{2\pi (300 \ rpm)}{60} = 31.42 \ rad/s$$

Integer Type Numericals for CBSE (Class 11 and 12):

1. Centripetal acceleration: $$a_c = \frac{v^2}{r}=\frac{(2 \ m/s)^2}{1 \ m} = 4 \ m/s^2$$

2. Centripetal acceleration: $$a_c = \frac{v^2}{r}=\frac{(9 \ km/h)^2}{(25 \ m)} = 3.24 \ m/s^2$$

3. Angular velocity: $$\omega = \frac{2\pi}{T}=\frac{2\pi \ rad}{20 \ s} = 0.314 \ rad/s$$

4. Linear speed: $$v = r\omega = (2 \ m)(0.5 \ rad/s) = 1 \ m/s$$

5. Angular velocity: $$\omega = \frac{2\pi N}{60}=\frac{2\pi (150 \ rpm)}{60} = 15.71 \ rad/s$$