Question

A body of mass 0.2 kg is attached to a light string of length 1 m and revolved in a vertical circle. What is the minimum speed at the lowest point so that the body can complete the circular motion? (Take \( g = 10 \, \text{m/s}^2 \))

• A. 2 m/s
• B. 4.47 m/s
• C. 5 m/s
• D. 6.32 m/s

Hint:

Remember: When applying energy principles, the minimum speed corresponds to the condition when the tension in the string is zero at the lowest point.

Answer 1

The Correct Option is B

Given: Mass of the body, \( m = 0.2 \, \text{kg} \) 
Length of the string, \( L = 1 \, \text{m} \)
Gravitational acceleration, \( g = 10 \, \text{m/s}^2 \)

Step 1: Conditions for Minimum Speed At the lowest point of the circular motion, the forces acting on the object are: - The tension in the string, \( T \) - The gravitational force, \( mg \) For the object to complete the circular motion, the centripetal force at the lowest point must be provided by the tension in the string and the gravitational force. The minimum speed required at the lowest point occurs when the tension in the string is zero, i.e., when the only force acting towards the center is the gravitational force. The equation for centripetal force at the lowest point is: \[ \frac{mv^2}{L} = T + mg \] At the minimum speed condition, \( T = 0 \), so: \[ \frac{mv^2}{L} = mg \] 

Step 2: Solve for Speed Simplifying the above equation: \[ v^2 = gL \] Substitute the values: \[ v^2 = (10 \, \text{m/s}^2)(1 \, \text{m}) = 10 \] \[ v = \sqrt{10} \approx 3.16 \, \text{m/s} \] 

Step 3: Conclusion Thus, the minimum speed at the lowest point for the body to complete the circular motion is approximately \( 3.16 \, \text{m/s} \). 

Answer: The closest option is (b) 4.47 m/s.