That's question 46 solve it in English

Here's the solution for Question 46: Question 46: Problem Statement: A ball of mass 0.4 kg is attached to a string of length 0.8 m. The ball is rotated in a vertical circle such that the speed at the lowest point is 6.0 m/s. The tension in the string at the lowest point is? Step 1: Identify the given values and the forces involved. Mass of the ball, m = 0.4 \, kg. Length of the string (which is the radius of the circular path), r = 0.8 \, m. Speed of the ball at the lowest point, v = 6.0 \, m/s. Acceleration due to gravity, g = 9.8 \, m/s^2. At the lowest point of the vertical circle, two forces act on the ball: 1. The tension (T) in the string, acting upwards (towards the center of the circle). 2. The gravitational force (mg), acting downwards (away from the center of the circle). Step 2: Apply Newton's Second Law for circular motion. The net force acting towards the center of the circle provides the centripetal force (F_c). At the lowest point, the centripetal force is the difference between the tension and the gravitational force. F_net = T - mg The centripetal force is given by F_c = (mv^2)/(r). Equating the net force to the centripetal force: T - mg = (mv^2)/(r) Step 3: Solve for the tension (T). Rearrange the equation to isolate T: T = mg + (mv^2)/(r) Substitute the given numerical values into the equation: T = (0.4 \, kg)(9.8 \, m/s^2) + (0.4 \, kg)(6.0 \, m/s)^20.8 \, m First, calculate the gravitational force: mg = 0.4 × 9.8 = 3.92 \, N Next, calculate the centripetal force term: (mv^2)/(r) = (0.4 × (6.0)^2)/(0.8) = (0.4 × 36)/(0.8) = (14.4)/(0.8) = 18 \, N Now, add these two values to find the tension: T = 3.92 \, N + 18 \, N T = 21.92 \, N Step 4: Compare the result with the given options. Rounding 21.92 \, N to two significant figures (consistent with the input values) gives 22 \, N. The given options are: (A) 4.0 N (B) 14 N (C) 18 N (D) 22 N The calculated tension matches option (D). The final answer is D. Drop the next question.