A particle is kept fixed on a turntable rotating uniformly. As seen from the ground the particle goes in a circle, its speed is 20 cm/s and acceleration is 20 . The particle is now shifted to a new position to make the radiushalf of the original value. The new values of the speed and acceleration will be

To find the new values of speed and acceleration, we can use the concept of centripetal acceleration and the relationship between speed, acceleration, and radius in circular motion.

1. Given information:

   • Initial speed (v1) = 20 cm/s
   • Initial acceleration (a1) = 20 cm/s^2
   • Initial radius (r1) = unknown

2. Using the formula for centripetal acceleration: a1 = (v1^2) / r1

3. Rearranging the formula to solve for r1: r1 = (v1^2) / a1

4. Substitute the given values: r1 = (20^2) / 20 = 400 / 20 = 20 cm

5. The initial radius is found to be 20 cm.

6. Now, we need to find the new values of speed and acceleration when the radius is halved.

7. Let's denote the new speed as v2 and the new acceleration as a2.

8. Using the relationship between speed, acceleration, and radius: v2 = (r1 / r2) * v1 a2 = (r1 / r2)^2 * a1

9. Substitute the known values: r1 = 20 cm (from step 5) r2 = r1 / 2 = 20 cm / 2 = 10 cm

10. Calculate the new speed: v2 = (20 cm / 10 cm) * 20 cm/s = 2 * 20 cm/s = 40 cm/s

11. Calculate the new acceleration: a2 = (20 cm / 10 cm)^2 * 20 cm/s^2 = 2^2 * 20 cm/s^2 = 4 * 20 cm/s^2 = 80 cm/s^2

12. The new values of speed and acceleration are: Speed (v2) = 40 cm/s Acceleration (a2) = 80 cm/s^2