Answer
64.8k+ views
Hint: We know that angular acceleration is the change in angular velocity divided by time, while tangential acceleration is the change in linear velocity divided by time. People sometimes forget that angular acceleration does not change with radius, but tangential acceleration does. Acceleration is a change in velocity, either in its magnitude that is speed or in its direction, or both. In uniform circular motion, the direction of the velocity changes constantly, so there is always an associated acceleration, even though the speed might be constant.
Complete step by step answer
The diagram for the given question is given as:
![](https://www.vedantu.com/question-sets/89350e97-df6c-4e6c-b23b-5dc649e8ee1a8714550367423786159.png)
We know that the concept of tangential acceleration is used to measure the change in the tangential velocity of a point with a specific radius with the change in time. Tangential acceleration is defined as the rate of change of tangential velocity of the matter in the circular path.
We know that tangential acceleration, $a_{1}=-g \sin \theta=-g \theta$
$-\quad a_{1}=-g^{\prime} \dfrac{x}{(R-r)}$
Motion is SHM is with time period $T=2 \pi \sqrt{\dfrac{\text { displacement }}{\text { acceleration }}}=2 \pi \sqrt{\dfrac{x}{\dfrac{g x}{(R-r)}}}=2 \pi \sqrt{\dfrac{R-r}{g}}$
So, the correct answer is option B.
Note: We can say that in physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. Since the object's velocity vector is constantly changing direction, the moving object is undergoing acceleration by a centripetal force in the direction of the center of rotation. Any time the speed of an object is changing, it has an acceleration. Angular acceleration is defined as the rate at which the angular velocity is changing. If the Ferris wheel speeds up at a constant rate, then we would say that the angular acceleration is constant.
Complete step by step answer
The diagram for the given question is given as:
![](https://www.vedantu.com/question-sets/89350e97-df6c-4e6c-b23b-5dc649e8ee1a8714550367423786159.png)
We know that the concept of tangential acceleration is used to measure the change in the tangential velocity of a point with a specific radius with the change in time. Tangential acceleration is defined as the rate of change of tangential velocity of the matter in the circular path.
We know that tangential acceleration, $a_{1}=-g \sin \theta=-g \theta$
$-\quad a_{1}=-g^{\prime} \dfrac{x}{(R-r)}$
Motion is SHM is with time period $T=2 \pi \sqrt{\dfrac{\text { displacement }}{\text { acceleration }}}=2 \pi \sqrt{\dfrac{x}{\dfrac{g x}{(R-r)}}}=2 \pi \sqrt{\dfrac{R-r}{g}}$
So, the correct answer is option B.
Note: We can say that in physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. Since the object's velocity vector is constantly changing direction, the moving object is undergoing acceleration by a centripetal force in the direction of the center of rotation. Any time the speed of an object is changing, it has an acceleration. Angular acceleration is defined as the rate at which the angular velocity is changing. If the Ferris wheel speeds up at a constant rate, then we would say that the angular acceleration is constant.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Other Pages
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
In the ground state an element has 13 electrons in class 11 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Electric field due to uniformly charged sphere class 12 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
According to classical free electron theory A There class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)