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A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8×10−4J by the end of the second revolution after the beginning of the motion?
- a)0.18m/s2
- b)0.2m/s2
- c)0.1m/s2
- d)0.15m/s2
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A particle of mass 10 g moves along a circle of radius 6.4 cm with a ...
To solve this problem, we can use the concept of work-energy theorem. The work-energy theorem states that the net work done on an object is equal to its change in kinetic energy. In this case, the net work done on the particle is responsible for the change in its kinetic energy.
Let's break down the problem into smaller steps:
Step 1: Calculate the initial kinetic energy of the particle
Given that the kinetic energy of the particle becomes equal to 8×10−4 J by the end of the second revolution, we can calculate the initial kinetic energy using the formula:
Initial kinetic energy = Final kinetic energy - Work done
Given that the final kinetic energy is 8×10−4 J, we need to calculate the work done.
Step 2: Calculate the work done on the particle
The work done on an object can be calculated using the formula:
Work done = Force × Distance × cos(θ)
In this case, the force is the net force acting on the particle, the distance is the circumference of the circle, and θ is the angle between the force and the displacement.
Since the particle moves along a circle, the net force acting on it is the centripetal force, given by:
Centripetal force = Mass × Acceleration
Step 3: Calculate the centripetal force
The centripetal force can be calculated using the formula:
Centripetal force = Mass × (Velocity^2 / Radius)
Given that the radius is 6.4 cm and the mass is 10 g (which is equal to 0.01 kg), we can calculate the centripetal force.
Step 4: Calculate the work done
Using the formula for work done, we can substitute the values of force, distance, and θ to calculate the work done.
Step 5: Calculate the initial kinetic energy
Using the work-energy theorem, we can substitute the values of the final kinetic energy and the work done to calculate the initial kinetic energy.
Step 6: Calculate the acceleration
Now that we know the initial kinetic energy, we can use the formula for kinetic energy to calculate the initial velocity. Then, we can use the formula for acceleration to calculate the acceleration.
The correct answer is option C) 0.1 m/s^2
Let's break down the problem into smaller steps:
Step 1: Calculate the initial kinetic energy of the particle
Given that the kinetic energy of the particle becomes equal to 8×10−4 J by the end of the second revolution, we can calculate the initial kinetic energy using the formula:
Initial kinetic energy = Final kinetic energy - Work done
Given that the final kinetic energy is 8×10−4 J, we need to calculate the work done.
Step 2: Calculate the work done on the particle
The work done on an object can be calculated using the formula:
Work done = Force × Distance × cos(θ)
In this case, the force is the net force acting on the particle, the distance is the circumference of the circle, and θ is the angle between the force and the displacement.
Since the particle moves along a circle, the net force acting on it is the centripetal force, given by:
Centripetal force = Mass × Acceleration
Step 3: Calculate the centripetal force
The centripetal force can be calculated using the formula:
Centripetal force = Mass × (Velocity^2 / Radius)
Given that the radius is 6.4 cm and the mass is 10 g (which is equal to 0.01 kg), we can calculate the centripetal force.
Step 4: Calculate the work done
Using the formula for work done, we can substitute the values of force, distance, and θ to calculate the work done.
Step 5: Calculate the initial kinetic energy
Using the work-energy theorem, we can substitute the values of the final kinetic energy and the work done to calculate the initial kinetic energy.
Step 6: Calculate the acceleration
Now that we know the initial kinetic energy, we can use the formula for kinetic energy to calculate the initial velocity. Then, we can use the formula for acceleration to calculate the acceleration.
The correct answer is option C) 0.1 m/s^2
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Community Answer
A particle of mass 10 g moves along a circle of radius 6.4 cm with a ...
Here,m = 10g = 10−2kg
R = 6.4cm = 6.4 × 10−2m, Kf = 8 × 10−4J
Ki = 0, at = ?
Using work energy theorem,
Work done by all the forces = Change in KE
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A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8×10−4J by the end of the second revolution after the beginning of the motion?a)0.18m/s2b)0.2m/s2c)0.1m/s2d)0.15m/s2Correct answer is option 'C'. Can you explain this answer?
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A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8×10−4J by the end of the second revolution after the beginning of the motion?a)0.18m/s2b)0.2m/s2c)0.1m/s2d)0.15m/s2Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8×10−4J by the end of the second revolution after the beginning of the motion?a)0.18m/s2b)0.2m/s2c)0.1m/s2d)0.15m/s2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8×10−4J by the end of the second revolution after the beginning of the motion?a)0.18m/s2b)0.2m/s2c)0.1m/s2d)0.15m/s2Correct answer is option 'C'. Can you explain this answer?.
A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8×10−4J by the end of the second revolution after the beginning of the motion?a)0.18m/s2b)0.2m/s2c)0.1m/s2d)0.15m/s2Correct answer is option 'C'. Can you explain this answer? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8×10−4J by the end of the second revolution after the beginning of the motion?a)0.18m/s2b)0.2m/s2c)0.1m/s2d)0.15m/s2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8×10−4J by the end of the second revolution after the beginning of the motion?a)0.18m/s2b)0.2m/s2c)0.1m/s2d)0.15m/s2Correct answer is option 'C'. Can you explain this answer?.
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