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A particle mass m is suspended from the ceiling through a string of length L. The partical moves in horizontal circle of radius r. speed of particle is?
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A particle mass m is suspended from the ceiling through a string of le...
Problem:

A particle mass m is suspended from the ceiling through a string of length L. The particle moves in a horizontal circle of radius r. What is the speed of the particle?


Solution:


To determine the speed of the particle, we need to consider the forces acting on it.


Forces acting on the particle:


  • The tension force of the string acting upwards.

  • The gravitational force acting downwards.

  • The centrifugal force acting outwards.



Equilibrium of forces:


The particle is moving in a horizontal circle, which means it is in equilibrium. The sum of all the forces acting on the particle is zero. So, we can write:

Fnet = T + mg + Fc = 0

where Fnet is the net force acting on the particle, T is the tension force of the string, mg is the gravitational force, and Fc is the centrifugal force.


Centrifugal force:


The centrifugal force is given by:

Fc = mv²/r

where m is the mass of the particle, v is the speed of the particle, and r is the radius of the circle.


Substitute equations:


Substituting the value of Fc in the equation for equilibrium of forces, we get:

T + mg + mv²/r = 0


Solve for speed:


Solving for v, we get:

v = √(gr/(r-L))


Final Answer:


Therefore, the speed of the particle is given by the equation v = √(gr/(r-L)), where g is the acceleration due to gravity.
Community Answer
A particle mass m is suspended from the ceiling through a string of le...
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Similar Class 12 Doubts

A cyclotron is a kind of particle accelerator invented by Ernest O. Lawrence at the University of California, Berkeley, in 1929–1930, and patented in 1932. A cyclotron accelerates charged particles along a spiral path outward from the center. The particles are guided by a static magnetic field to a spiral trajectory, and accelerated by a rapidly changing electric field (radio frequency). For this invention Lawrence received the 1939 Nobel Prize in Physics.Cyclotrons were the most efficient particle accelerator equipment until the 1950s, when the synchrotron replaced them, and are now used in science and nuclear medicine to generate particle beams.This will toss the particle out of resonance with the oscillating field which means that when the particle reaches the hole between the dees, the extremity of the dees won't change. Thus, the particle won't be accelerated further.So, Cyclotron isn't reasonable for accelerating electrons. Because of the small mass, the speed of electrons increments quickly. Similarly, because of fast relativistic variation in their mass, the electrons escape step with the oscillating electric field.Hence, option A is the correct option.

A particle mass m is suspended from the ceiling through a string of length L. The partical moves in horizontal circle of radius r. speed of particle is?
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A particle mass m is suspended from the ceiling through a string of length L. The partical moves in horizontal circle of radius r. speed of particle is? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A particle mass m is suspended from the ceiling through a string of length L. The partical moves in horizontal circle of radius r. speed of particle is? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A particle mass m is suspended from the ceiling through a string of length L. The partical moves in horizontal circle of radius r. speed of particle is?.
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