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Question
1) A bob of mass m suspended by a light string of length L is whirled into a vertical circle as shown in figure. What will be the trajectory of the particle if the string is cut at point B ?
2) A bob of mass m suspended by a light string of length L is whirled into a vertical circle as shown in figure. What will be the trajectory of the particle if the string is cut at point C ?
3) A bob of mass m suspended by a light string of length L is whirled into a vertical circle as shown in figure. What will be the trajectory of the particle if the string is cut at point X ?
2) A bob of mass m suspended by a light string of length L is whirled into a vertical circle as shown in figure. What will be the trajectory of the particle if the string is cut at point C ?
3) A bob of mass m suspended by a light string of length L is whirled into a vertical circle as shown in figure. What will be the trajectory of the particle if the string is cut at point X ?
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Solution
1) When the bob is whirled into circular path the required centripetal force is provided by the tension in the string (towards the centre of the circular path) and it is balanced by the centrifugal force.
When string is cut, tension in string becomes zero and centripetal force is not provided. Hence bob tends to move with tangential velocity under gravity.
At point B tangential velocity will be vertically downwards, so bob will move along vertical path under gravity.
Final answer: Straight line: vertical, downwards
2) When the bob is whirled into circular path the required centripetal force is provided by the tension in the string (towards the centre of the circular path) and it is balanced by the centrifugal force.
When string is cut, tension in string becomes zero and centripetal force is not provided. Hence bob tends to move with tangential velocity under gravity.
At point C tangential velocity will be horizontally right, so bob will move along parabolic path under gravity.
Final answer: parabolic path
3) When the bob is whirled into circular path the required centripetal force is provided by the tension in the string (towards the centre of the circular path) and it is balanced by the centrifugal force provided by tangential velocity of the particle.
When string is cut, tension in string becomes zero and centripetal force is not provided. Hence bob tends to move with tangential velocity under gravity.
At point X tangential velocity makes some angle with horizontal, so bob will move along parabolic path with vertex higher than C under gravity.
Final answer: parabolic path with vertex higher than C.
When string is cut, tension in string becomes zero and centripetal force is not provided. Hence bob tends to move with tangential velocity under gravity.
At point B tangential velocity will be vertically downwards, so bob will move along vertical path under gravity.
Final answer: Straight line: vertical, downwards
2) When the bob is whirled into circular path the required centripetal force is provided by the tension in the string (towards the centre of the circular path) and it is balanced by the centrifugal force.
When string is cut, tension in string becomes zero and centripetal force is not provided. Hence bob tends to move with tangential velocity under gravity.
At point C tangential velocity will be horizontally right, so bob will move along parabolic path under gravity.
Final answer: parabolic path
3) When the bob is whirled into circular path the required centripetal force is provided by the tension in the string (towards the centre of the circular path) and it is balanced by the centrifugal force provided by tangential velocity of the particle.
When string is cut, tension in string becomes zero and centripetal force is not provided. Hence bob tends to move with tangential velocity under gravity.
At point X tangential velocity makes some angle with horizontal, so bob will move along parabolic path with vertex higher than C under gravity.
Final answer: parabolic path with vertex higher than C.
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