“Vertical Circular Motion” MHT-CET Class 12 Physics Crash Course| Chapter Rotational Dynamics
In this session G.S. Khairnar will discuss the theory and MCQ’s of “Vertical Circular Motion”. The session will be useful for all the aspirants of MHT-CET 2022. The session will be in Marathi and English.
Vertical Circular Motion:-
Hello everyone, we know that in circular motion is divided in to uniform circular motion and non uniform circular motion. During vertical circular motion, velocity of object at every point is different in magnitude as well as magnitude, thus it is non-uniform circular motion.
e.g. children enjoying motion in giant wheel is example of vertical circular motion. In giant wheel, when we are moving from top to bottom velocity increases so as to increase the kinetic energy, whereas during motion from bottom to top velocity decreases but potential energy increase. According to law of conservation of energy, total energy in vertical circular motion always remains conserved.
Let’s discuss the concept of conical pendulum in detail……!
Consider an object of mass ‘m’ tied at the one end of an inextensible string & whirled in vertical circle of radius ‘r’. Due to the influence of earth’s gravitational field, its velocity & tension vary in magnitude. It is maximum (V2) at lowest point & minimum (V1) at highest point as shown in fig. below,
At point A (highest point) centripetal force is provided by tension T1 in the string & weight of the body.
At lowest point ‘B’ tension T2& weight ‘mg’ are opposite in directions hence (T2–mg) provides necessary centripetal force.
Linear velocity (v1) at highest point (A)
There is certain minimum velocity v1 of object at A below which string becomes slack.
i.e. Tension T1 vanishes.
Linear velocity (v2) at lowest point (B)
Linear velocity (v3) at lowest point (C)
Some important terms-
1) Energy of particle in vertical circular motion at any point is always constant and is given by formula,
2) The difference in tensions at the lowest and highest position in vertical circular motion is
TL – TH = 6mg
3) The difference in tensions at the lowest and midway position in vertical circular motion is
TL – TM = 3mg
Vertical Circular Motion
Lets learn the following MCQ’s…
Q.1) If particle of mass ‘m’ tied to string performing vertical circular motion with velocity ‘v’, tension ‘T’ and radius ‘r’ is at highest position in circular motion, which among the following is correct equation?
Q.1) If particle of mass ‘m’ tied to string performing vertical circular motion with velocity ‘v’, tension ‘T’ and radius ‘r’ is at highest position in circular motion, which among the following is correct equation?
Q.3) A particle performing vertical circular motion of radius ‘r’ and velocity ‘v’. To maintain the vertical circle, value of tension at the highest position should be…
a) infinitely high
b) high
c) low
d) almost equal to zero
Answer
d) almost equal to zero
Q.4) A bucket containing water whirled in vertical circular motion at radius of 1.2 m. Velocity at highest position is…
a) 3.43 cm/s
b) 3.43 m/s
c) 3.43 km/s
d) 3.43 rad/s
Answer
b) 3.43 m/s
Q.5) Energy of particle in vertical circular motion at any point is……………
Q.6) The difference in tensions at the lowest and highest position in vertical circular motion is ……………
Q.7) An object of mass 200 g is tied to string of length 1.5 m is whirled in vertical circle, the velocity of object at lowest position is……………
a) 8.6 m/s
b) 8.6 cm/s
c) 86 m/s
d) 86 cm/s
Answer
a) 8.6 m/s
Q.8) The difference in tensions at the lowest and midway position in vertical circular motion is ……………
a) 0
b) mg
c) 3mg
d) 6 mg
Answer
c) 3mg
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