Question:
A body of mass 1 kg is attached to one end of a string of 1 m length. It is rotated in a vertical circle with a constant speed of \( 4 \text{ ms}^{-1} \). When the object is at the highest point of the vertical circle, tension in the string is (\( g=10 \text{ ms}^{-2} \)):
A body of mass 1 kg is attached to one end of a string of 1 m length. It is rotated in a vertical circle with a constant speed of \( 4 \text{ ms}^{-1} \). When the object is at the highest point of the vertical circle, tension in the string is (\( g=10 \text{ ms}^{-2} \)):
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At the lowest point of a vertical circle, tension is at its maximum (\(T_{max} = \frac{mv^2}{r} + mg\)), whereas at the highest point, tension is at its minimum (\(T_{min} = \frac{mv^2}{r} - mg\)).
Updated On: Jun 9, 2026
- \( 6 \text{ N} \)
- \( 8 \text{ N} \)
- \( 10 \text{ N} \)
- \( 16 \text{ N} \)
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The Correct Option is A
Solution and Explanation
Concept:
When a body rotates in a vertical circle, the net centripetal force required to maintain circular motion at any point is provided by the vector sum of the forces acting radially toward the center. At the highest point of the vertical circle, both the gravitational force (acting downwards) and the tension in the string (acting downwards, toward the center) contribute to the centripetal force.
Step 1: Identify the forces at the highest point.
At the highest point, the forces directed toward the center are: 1. The tension in the string, \( T \). 2. The component of gravitational force acting radially inward, which is equal to the weight \( mg \) since the string is vertical.
Step 2: Formulate the equation of motion.
According to Newton's Second Law for circular motion, the net radial force must equal the required centripetal force (\( F_c = \frac{mv^2}{r} \)): $$ T + mg = \frac{mv^2}{r} $$
Step 3: Substitute the known physical parameters.
Given: Mass \( m = 1 \text{ kg} \) Length of string (radius) \( r = 1 \text{ m} \) Velocity \( v = 4 \text{ ms}^{-1} \) Acceleration due to gravity \( g = 10 \text{ ms}^{-2} \) Substituting these into our force equation: $$ T + (1 \text{ kg} \times 10 \text{ ms}^{-2}) = \frac{1 \text{ kg} \times (4 \text{ ms}^{-1})^2}{1 \text{ m}} $$ $$ T + 10 \text{ N} = \frac{16}{1} \text{ N} $$
Step 4: Solve for the tension.
$$ T = 16 \text{ N} - 10 \text{ N} $$ $$ T = 6 \text{ N} $$ $$\boxed{6 \text{ N}}$$
Step 1: Identify the forces at the highest point.
At the highest point, the forces directed toward the center are: 1. The tension in the string, \( T \). 2. The component of gravitational force acting radially inward, which is equal to the weight \( mg \) since the string is vertical.
Step 2: Formulate the equation of motion.
According to Newton's Second Law for circular motion, the net radial force must equal the required centripetal force (\( F_c = \frac{mv^2}{r} \)): $$ T + mg = \frac{mv^2}{r} $$
Step 3: Substitute the known physical parameters.
Given: Mass \( m = 1 \text{ kg} \) Length of string (radius) \( r = 1 \text{ m} \) Velocity \( v = 4 \text{ ms}^{-1} \) Acceleration due to gravity \( g = 10 \text{ ms}^{-2} \) Substituting these into our force equation: $$ T + (1 \text{ kg} \times 10 \text{ ms}^{-2}) = \frac{1 \text{ kg} \times (4 \text{ ms}^{-1})^2}{1 \text{ m}} $$ $$ T + 10 \text{ N} = \frac{16}{1} \text{ N} $$
Step 4: Solve for the tension.
$$ T = 16 \text{ N} - 10 \text{ N} $$ $$ T = 6 \text{ N} $$ $$\boxed{6 \text{ N}}$$
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