Centripetal Acceleration

Minimum Speed for Circular Motion

We are given the following information:

• Mass of the body
• Length of the string
• Acceleration due to gravity

Step 1: Recall the conditions for circular motion.

For a body to complete the circular motion, the tension in the string at the highest point should be greater than or equal to zero. At the highest point, the only forces acting on the body are the gravitational force and the tension , and they must provide the centripetal force to keep the body in circular motion.

At the lowest point, the body must have sufficient speed to maintain the circular motion, and the minimum speed occurs when the tension at the highest point is zero. In other words, the gravitational force alone provides the necessary centripetal force at the highest point.

Step 2: Using the centripetal force equation at the highest point.

The centripetal force required at the highest point is:

where is the velocity at the highest point, is the mass, is the length of the string (radius of the circular motion), and is the acceleration due to gravity.

Step 3: Solve for the minimum speed.

From the equation above, we can solve for (the minimum speed at the lowest point):

Substitute the values:

Conclusion:

The minimum speed at the lowest point for the body to complete the circular motion is approximately .

Given: Velocity of the particle,
Radius of the circular path,

Step 1: Formula for Centripetal Acceleration The centripetal acceleration is given by the formula: where: - is the velocity, - is the radius.

Step 2: Substitute the given values Substitute the given values into the formula:

Step 3: Conclusion Thus, the centripetal acceleration of the particle is .

Answer: The correct answer is option (d): 10 m/s .

Given:

• Radius
• Speed

Step 1: Use the formula for centripetal acceleration

The formula for centripetal acceleration is:

where: - is the centripetal acceleration, - is the speed of the object, - is the radius of the circular path.

Step 2: Substitute the given values into the formula

✅ Final Answer:

The centripetal acceleration of the body is .