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A particle originally at rest at highest point of smooth verticle circle of radius R is slightly displace it will live the circle at distance H below highest point. find its position .?
Ref: https://edurev.in/question/437917/A-particle-originally-at-rest-at-highest-point-of-smooth-verticle-circle-of-radius-R-is-slightly-dis

Question: A particle is originally at rest at the highest point of a smooth vertical circle of radius R. If the particle is slightly displaced, the distance below the highest point where the particle will leave the circle is
Ans:
Problem (with Solution): Circular motion - JEE
Suppose the particle leaves the circle at distance h below the highest point.
The point where it leaves the circle reaction force(N)=0
therefore mgcosθ = mv2/R
or cosθ =v2/Rg
Now applying conservation of energy

mgh = (1/2)mv2

or v= 2gh

therefore cosθ = 2h/R

by geometry

cosθ = R-h/R,

therefore R-h/R = 2h/R or h = R/3

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FAQs on Problem (with Solution): Circular motion - JEE

1. What is circular motion in the context of JEE?
Ans. Circular motion refers to the movement of an object along a circular path. In the context of JEE, it is a topic in physics that deals with the principles and calculations related to objects moving in a circular path, such as centripetal force, angular velocity, and acceleration.
2. How is centripetal force related to circular motion?
Ans. Centripetal force is the force that acts towards the center of the circular path to keep an object in circular motion. It is responsible for changing the direction of the object's velocity, without affecting its speed. The magnitude of the centripetal force can be calculated using the equation F = (mv^2)/r, where F is the force, m is the mass of the object, v is its velocity, and r is the radius of the circular path.
3. Can you explain the concept of angular velocity in circular motion?
Ans. Angular velocity is a measure of how fast an object is rotating around a fixed point in circular motion. It is defined as the change in angle per unit time. Mathematically, angular velocity (ω) is given by the equation ω = Δθ/Δt, where Δθ is the change in angle and Δt is the change in time. The unit of angular velocity is radians per second (rad/s).
4. What is the difference between uniform circular motion and non-uniform circular motion?
Ans. Uniform circular motion refers to the circular motion in which the speed of the object remains constant, but the direction of motion continuously changes. In this case, the magnitude of the velocity remains constant, while the direction changes. On the other hand, non-uniform circular motion refers to the circular motion in which both the speed and the direction of the object change. In this case, the magnitude and direction of the velocity change.
5. How can we calculate the acceleration in circular motion?
Ans. The acceleration in circular motion can be calculated using the equation a = v^2/r, where a is the acceleration, v is the velocity of the object, and r is the radius of the circular path. This equation represents the centripetal acceleration, which is always directed towards the center of the circular path.
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