Answer
Verified
447.9k+ views
Hint:-Recall the concept of angular velocity. It is the velocity at which the particle rotates around a canter or a point in the given time. It is also known as rotational velocity. It shows how fast the position of an object changes with time.
Complete step-by-step solution:
Step I:
Given that time $t = 2\sec $
$N1 = 60rpm$
1minute = 60seconds
$60rpm = \dfrac{{60}}{{60}} = 1 revolution per second$
Similarly $N2 = 120rpm$
$120rpm = \dfrac{{120}}{{60}} = 2 revolution per seconds$
Step II:
Formula for angular velocity is written as $\omega = 2n\pi $
Where $\omega $ is the angular velocity
${\omega _1} = 2{n_1}\pi $
${\omega _1} = 2 \times 1 \times \pi $
${\omega _1} = 2\pi rad/\sec $
Similarly, ${\omega _2} = 2 \times N2 \times \pi $
${\omega _2} = 2 \times 2 \times \pi $
${\omega _2} = 4\pi rad/\sec $
Step III:
Also the angular acceleration of the body is given by
$ \propto = \dfrac{{{\omega _2} - {\omega _1}}}{T}$
$ \propto = \dfrac{{4\pi - 2\pi }}{2}$
$ \propto = \dfrac{{2\pi }}{2}$
$ \propto = \pi rad/{\sec ^2}$
Step IV:
Angular displacement is the shortest angle between the initial and final positions for a given object having circular motion. It has both magnitude and direction. It is the angle of movement of a body in the circular path. So it is a vector quantity. It is known that if the angular acceleration, initial velocity and time are given, then angular displacement can be calculated using the formula
$\theta = \omega t + \dfrac{1}{2} \propto {t^2}$
Where $\theta $ is angular displacement
$\omega $ is the initial angular velocity
$t$ is the time taken
$ \propto $ is the angular acceleration
$\theta = 2\pi \times 2 + \dfrac{1}{2}\pi {(2)^2}$
$\theta = 4\pi + 2\pi $
$\theta = 6\pi $
Step V:
To measure an angle, a radian is used. There are $2\pi $ radians in one complete revolution. Hence,
Number of revolutions is given by $ = \dfrac{{6\pi }}{{2\pi }} = 3$.
Option C is the right answer.
Note:- It is to be noted that the terms angular acceleration and radial acceleration are different terms. Angular acceleration is the rate of change of angular velocity with time. An object with angular velocity will either rotate faster or slower. On the other hand, when an object undergoes circular motion then it shows radial acceleration.
Complete step-by-step solution:
Step I:
Given that time $t = 2\sec $
$N1 = 60rpm$
1minute = 60seconds
$60rpm = \dfrac{{60}}{{60}} = 1 revolution per second$
Similarly $N2 = 120rpm$
$120rpm = \dfrac{{120}}{{60}} = 2 revolution per seconds$
Step II:
Formula for angular velocity is written as $\omega = 2n\pi $
Where $\omega $ is the angular velocity
${\omega _1} = 2{n_1}\pi $
${\omega _1} = 2 \times 1 \times \pi $
${\omega _1} = 2\pi rad/\sec $
Similarly, ${\omega _2} = 2 \times N2 \times \pi $
${\omega _2} = 2 \times 2 \times \pi $
${\omega _2} = 4\pi rad/\sec $
Step III:
Also the angular acceleration of the body is given by
$ \propto = \dfrac{{{\omega _2} - {\omega _1}}}{T}$
$ \propto = \dfrac{{4\pi - 2\pi }}{2}$
$ \propto = \dfrac{{2\pi }}{2}$
$ \propto = \pi rad/{\sec ^2}$
Step IV:
Angular displacement is the shortest angle between the initial and final positions for a given object having circular motion. It has both magnitude and direction. It is the angle of movement of a body in the circular path. So it is a vector quantity. It is known that if the angular acceleration, initial velocity and time are given, then angular displacement can be calculated using the formula
$\theta = \omega t + \dfrac{1}{2} \propto {t^2}$
Where $\theta $ is angular displacement
$\omega $ is the initial angular velocity
$t$ is the time taken
$ \propto $ is the angular acceleration
$\theta = 2\pi \times 2 + \dfrac{1}{2}\pi {(2)^2}$
$\theta = 4\pi + 2\pi $
$\theta = 6\pi $
Step V:
To measure an angle, a radian is used. There are $2\pi $ radians in one complete revolution. Hence,
Number of revolutions is given by $ = \dfrac{{6\pi }}{{2\pi }} = 3$.
Option C is the right answer.
Note:- It is to be noted that the terms angular acceleration and radial acceleration are different terms. Angular acceleration is the rate of change of angular velocity with time. An object with angular velocity will either rotate faster or slower. On the other hand, when an object undergoes circular motion then it shows radial acceleration.
Recently Updated Pages
what is the correct chronological order of the following class 10 social science CBSE
Which of the following was not the actual cause for class 10 social science CBSE
Which of the following statements is not correct A class 10 social science CBSE
Which of the following leaders was not present in the class 10 social science CBSE
Garampani Sanctuary is located at A Diphu Assam B Gangtok class 10 social science CBSE
Which one of the following places is not covered by class 10 social science CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The only snake that builds a nest is a Krait b King class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Why is there a time difference of about 5 hours between class 10 social science CBSE
Which places in India experience sunrise first and class 9 social science CBSE