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 beA 10 cm/s, 10  B 10 cm/s, 80  C 40 cm/s, 10  D 40 cm/s, 40

To solve this problem, let's break it down step by step:

Step 1: Given information

• The particle is fixed on a turntable rotating uniformly.
• The speed of the particle is 20 cm/s.
• The acceleration of the particle is 20.

Step 2: Relationship between speed, acceleration, and radius In circular motion, there is a relationship between speed (v), acceleration (a), and radius (r) given by the equation: a = v^2 / r

Step 3: Finding the original radius Using the given information, we can rearrange the equation to solve for the original radius (r): r = v^2 / a r = (20 cm/s)^2 / 20 r = 400 cm

Step 4: Finding the new radius The problem states that the new radius is half of the original value. Therefore, the new radius (r') is: r' = 400 cm / 2 r' = 200 cm

Step 5: Finding the new speed To find the new speed (v'), we can use the relationship between speed, acceleration, and radius: a = v'^2 / r' 20 = v'^2 / 200 v'^2 = 20 * 200 v' = √(20 * 200) v' ≈ 28.28 cm/s

Step 6: Finding the new acceleration Since the acceleration remains the same, the new acceleration (a') is also 20.

Step 7: Answering the question The new values of speed and acceleration are approximately 28.28 cm/s and 20, respectively.

Therefore, the correct answer is option D: 40 cm/s, 40.