Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A nail is located at a certain distance vertically below the point of suspension of a simple pendulum. The pendulum bob is released from the position where the string makes an angle of 60° from the vertical. Calculate the distance of the nail from the point of suspension such that bob will just perform revolution with the nail as centre. Assume the length of pendulum to be 1m.
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: Understand the situation.
In this problem, we have a simple pendulum with a length (L) of 1 meter. The bob is released from an angle of 60° with the vertical, and we need to find the height (h) of the nail below the point of suspension such that the bob performs a complete revolution around the nail.
Step 2: Analyze the forces acting on the bob.
When the bob swings and reaches the nail, it must have enough kinetic energy to complete a circular motion around it. For the bob to just make the circular path around the nail, the centripetal force should be provided by the component of the gravitational force acting on the bob at the topmost position of the swing.
Step 3: Determine the height at which the bob has potential energy and will convert to kinetic energy.
When the bob is released from 60°, the vertical height (h) gained from the lowest point while swinging down can be calculated using:
$$ h = L(1 - ext{cos}(60^ ext{o})) $$
Since L = 1 m:
$$ h = 1(1 - ext{cos}(60^ ext{o})) = 1(1 - 0.5) = 0.5 ext{ m} $$
Step 4: Assess the distance from the point of suspension to the nail.
The bob must rotate around the nail, meaning the nail must be situated at this vertical (half a meter) point. Hence, the distance from the point of suspension to the point of nail is 0.5 m. Therefore:
$$ h = rac{L}{2} = rac{1}{2} ext{ m} $$
Thus, the required distance of the nail from the point of suspension is 0.5 m.
Step 5: Conclusion.
Therefore, the nail should be located at a distance of 0.5 meters below the point of suspension for the pendulum bob to perform a complete revolution.
In this problem, we have a simple pendulum with a length (L) of 1 meter. The bob is released from an angle of 60° with the vertical, and we need to find the height (h) of the nail below the point of suspension such that the bob performs a complete revolution around the nail.
Step 2: Analyze the forces acting on the bob.
When the bob swings and reaches the nail, it must have enough kinetic energy to complete a circular motion around it. For the bob to just make the circular path around the nail, the centripetal force should be provided by the component of the gravitational force acting on the bob at the topmost position of the swing.
Step 3: Determine the height at which the bob has potential energy and will convert to kinetic energy.
When the bob is released from 60°, the vertical height (h) gained from the lowest point while swinging down can be calculated using:
$$ h = L(1 - ext{cos}(60^ ext{o})) $$
Since L = 1 m:
$$ h = 1(1 - ext{cos}(60^ ext{o})) = 1(1 - 0.5) = 0.5 ext{ m} $$
Step 4: Assess the distance from the point of suspension to the nail.
The bob must rotate around the nail, meaning the nail must be situated at this vertical (half a meter) point. Hence, the distance from the point of suspension to the point of nail is 0.5 m. Therefore:
$$ h = rac{L}{2} = rac{1}{2} ext{ m} $$
Thus, the required distance of the nail from the point of suspension is 0.5 m.
Step 5: Conclusion.
Therefore, the nail should be located at a distance of 0.5 meters below the point of suspension for the pendulum bob to perform a complete revolution.
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