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Particle p,mass m,moving on smooth circular wire of radius 5cm being acted upon by attractive forces dirrected towards o which is 3cm from c ,having magnitude 4m/3(op)^2 dynezs find the minmum velocity which should be given to the particle at a ?so that ,it may complete the circle sucessfully.Neglect gravity.?
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Problem:
A particle of mass m is moving on a smooth circular wire of radius 5 cm. The particle is acted upon by attractive forces directed towards point O, which is located 3 cm from the center of the circle. The magnitude of the force is given by 4m/3(op)^2 dynezs. We need to find the minimum velocity that should be given to the particle at point A so that it may complete the circle successfully, neglecting gravity.
Solution:
To solve this problem, we will analyze the forces acting on the particle and use the principles of circular motion.
1. Centripetal Force:
The particle is moving in a circular path, so there must be a centripetal force acting towards the center of the circle. This force is provided by the attractive forces directed towards point O. The magnitude of this force is given by 4m/3(op)^2 dynezs.
2. Centripetal Acceleration:
The centripetal force is responsible for providing the necessary centripetal acceleration to keep the particle on its circular path. The centripetal acceleration is given by the equation:
a = v^2 / r
where v is the velocity of the particle and r is the radius of the circular path.
3. Equating Centripetal Force and Centripetal Acceleration:
Equating the centripetal force and centripetal acceleration, we get:
4m/3(op)^2 = m * v^2 / r
4. Simplifying and Solving for v:
Simplifying the equation, we can cancel out the mass m and rearrange to solve for v:
v^2 = (4/3) * (op)^2 * r
v = sqrt((4/3) * (op)^2 * r)
5. Substituting Values:
Substituting the given values into the equation, we have:
v = sqrt((4/3) * (3)^2 * 5) = sqrt(4 * 9 * 5) = sqrt(180) = 6sqrt(5) cm/s
Therefore, the minimum velocity that should be given to the particle at point A is 6sqrt(5) cm/s.
A particle of mass m is moving on a smooth circular wire of radius 5 cm. The particle is acted upon by attractive forces directed towards point O, which is located 3 cm from the center of the circle. The magnitude of the force is given by 4m/3(op)^2 dynezs. We need to find the minimum velocity that should be given to the particle at point A so that it may complete the circle successfully, neglecting gravity.
Solution:
To solve this problem, we will analyze the forces acting on the particle and use the principles of circular motion.
1. Centripetal Force:
The particle is moving in a circular path, so there must be a centripetal force acting towards the center of the circle. This force is provided by the attractive forces directed towards point O. The magnitude of this force is given by 4m/3(op)^2 dynezs.
2. Centripetal Acceleration:
The centripetal force is responsible for providing the necessary centripetal acceleration to keep the particle on its circular path. The centripetal acceleration is given by the equation:
a = v^2 / r
where v is the velocity of the particle and r is the radius of the circular path.
3. Equating Centripetal Force and Centripetal Acceleration:
Equating the centripetal force and centripetal acceleration, we get:
4m/3(op)^2 = m * v^2 / r
4. Simplifying and Solving for v:
Simplifying the equation, we can cancel out the mass m and rearrange to solve for v:
v^2 = (4/3) * (op)^2 * r
v = sqrt((4/3) * (op)^2 * r)
5. Substituting Values:
Substituting the given values into the equation, we have:
v = sqrt((4/3) * (3)^2 * 5) = sqrt(4 * 9 * 5) = sqrt(180) = 6sqrt(5) cm/s
Therefore, the minimum velocity that should be given to the particle at point A is 6sqrt(5) cm/s.
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Particle p,mass m,moving on smooth circular wire of radius 5cm being acted upon by attractive forces dirrected towards o which is 3cm from c ,having magnitude 4m/3(op)^2 dynezs find the minmum velocity which should be given to the particle at a ?so that ,it may complete the circle sucessfully.Neglect gravity.?
Question Description
Particle p,mass m,moving on smooth circular wire of radius 5cm being acted upon by attractive forces dirrected towards o which is 3cm from c ,having magnitude 4m/3(op)^2 dynezs find the minmum velocity which should be given to the particle at a ?so that ,it may complete the circle sucessfully.Neglect gravity.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Particle p,mass m,moving on smooth circular wire of radius 5cm being acted upon by attractive forces dirrected towards o which is 3cm from c ,having magnitude 4m/3(op)^2 dynezs find the minmum velocity which should be given to the particle at a ?so that ,it may complete the circle sucessfully.Neglect gravity.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Particle p,mass m,moving on smooth circular wire of radius 5cm being acted upon by attractive forces dirrected towards o which is 3cm from c ,having magnitude 4m/3(op)^2 dynezs find the minmum velocity which should be given to the particle at a ?so that ,it may complete the circle sucessfully.Neglect gravity.?.
Particle p,mass m,moving on smooth circular wire of radius 5cm being acted upon by attractive forces dirrected towards o which is 3cm from c ,having magnitude 4m/3(op)^2 dynezs find the minmum velocity which should be given to the particle at a ?so that ,it may complete the circle sucessfully.Neglect gravity.? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Particle p,mass m,moving on smooth circular wire of radius 5cm being acted upon by attractive forces dirrected towards o which is 3cm from c ,having magnitude 4m/3(op)^2 dynezs find the minmum velocity which should be given to the particle at a ?so that ,it may complete the circle sucessfully.Neglect gravity.? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Particle p,mass m,moving on smooth circular wire of radius 5cm being acted upon by attractive forces dirrected towards o which is 3cm from c ,having magnitude 4m/3(op)^2 dynezs find the minmum velocity which should be given to the particle at a ?so that ,it may complete the circle sucessfully.Neglect gravity.?.
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