The centripetal acceleration of the ball swung in a horizontal circle is approximately 2.96 m/s^2.
The correct answer is option C.
Centripetal acceleration (ac) can be calculated using the formula ac = v^2 / r, where v is the speed and r is the radius of the circular motion. In this case, since the ball is swung in a horizontal circle at a constant speed, the speed (v) can be determined from the time it takes to complete one circle.
The time to complete one circle (T) is given as 0.85 seconds, and the radius of the circle (r) is the length of the rope, which is 0.40 meters.
The formula for speed is v = (2πr) / T, where 2πr is the circumference of the circle.
v = (2π × 0.40) / 0.85
Calculating this gives the speed (v).
Once v is found, we can use the centripetal acceleration formula ac = v^2 / r.
ac = v^2 / 0.40
Substituting the calculated value of v, we get:
ac = ((2π × 0.40) / 0.85)^2 / 0.40
Calculating this expression gives the centripetal acceleration.
ac is approximately 2.96 m/s^2.
Therefore, the centripetal acceleration is approximately 2.96 m/s^2.
Hence , the correct answer is option C.