Answer
396.9k+ views
Hint: Here, we will use the basic concept of impulse-momentum theorem and then we will use the equation to find the final velocity of the particle. We will further study how friction affects the motion of an object or particle. This will give us the required result.
Formula used:
\[\begin{align}
& J=\Delta P \\
& \Rightarrow J=M{v}'+mV \\
\end{align}\]
Complete answer:
Since, the impulse momentum theorem can be stated as: a collision, when an object experiences a force for a given amount of time (small duration) that results in its mass undergoing a change in velocity. Here the momentum of the two collision particles changes.
From the impulse momentum theorem, the impulse imparted by the ball is J and v is the initial velocity and v’ is the final velocity.
\[\begin{align}
& J=\Delta P \\
& \Rightarrow J=M{v}'-m\left( -V \right) \\
& \Rightarrow J=M{v}'+mV \\
& \Rightarrow J\times 0.25=M{{R}^{2}}\left( {{\omega }_{f}} \right)-M{{R}^{2}}\left( \dfrac{v}{R} \right) \\
& \Rightarrow J=4M{{R}^{2}}\left( {{\omega }_{f}} \right)+4M{{R}^{2}}\left( \dfrac{v}{R} \right) \\
& \Rightarrow 4M{{R}^{2}}{{\omega }_{f}}+4MRv=M{v}'+Mv \\
\end{align}\]
Substituting the given values in above equation we get:
\[\begin{align}
& 4\times \dfrac{5}{10}\times \dfrac{8}{10}{{\omega }_{f}}+4\times \dfrac{8}{10}\times 1={v}'+1 \\
& \Rightarrow {v}'={{\omega }_{f}}+1 \\
& \because 2R{{\omega }_{f}}+1={v}' \\
& \therefore {v}'\rangle {{\omega }_{f}}f \\
\end{align}\]
Therefore, we can say from the result that the friction between the ring and the ground is to the left.
Additional information:
As we know that, the friction force is defined as the force exerted by a surface as an object moves across it or makes an effort to move across it. There are mainly three types of friction forces: sliding friction, static friction and the last one rolling friction.
Static friction comes into action on objects when they are resting on a surface. For example, if we are hiking in the woods, there is a presence of static friction between our shoes and the trail each time we put down our foot. Without this friction, our feet would slip out and thereby, making it difficult to walk.
Sliding friction is friction that comes in action on objects when they are sliding over another surface. As we know that the sliding friction is weaker than the static friction. That is the reason that it is easier to slide a piece of furniture over the floor after we start it moving than it is to get it moving in the first place.
The last one is rolling friction is friction that comes in action on objects when they are rolling over another surface. Rolling friction is much weaker than sliding friction and static friction. This is the reason that most forms of ground transportation use wheels, including bicycles, cars, 4-wheelers, roller skates, scooters, and skateboards, as these wheels make it easier to travel with facing less frictional force.
Note:
Frictional force is a force that opposes the motion of any object. There are many practical examples of frictional force. We should also remember that various kinds of lubricants are used to overcome the frictional force like- grease, oil etc.
Formula used:
\[\begin{align}
& J=\Delta P \\
& \Rightarrow J=M{v}'+mV \\
\end{align}\]
Complete answer:
Since, the impulse momentum theorem can be stated as: a collision, when an object experiences a force for a given amount of time (small duration) that results in its mass undergoing a change in velocity. Here the momentum of the two collision particles changes.
From the impulse momentum theorem, the impulse imparted by the ball is J and v is the initial velocity and v’ is the final velocity.
\[\begin{align}
& J=\Delta P \\
& \Rightarrow J=M{v}'-m\left( -V \right) \\
& \Rightarrow J=M{v}'+mV \\
& \Rightarrow J\times 0.25=M{{R}^{2}}\left( {{\omega }_{f}} \right)-M{{R}^{2}}\left( \dfrac{v}{R} \right) \\
& \Rightarrow J=4M{{R}^{2}}\left( {{\omega }_{f}} \right)+4M{{R}^{2}}\left( \dfrac{v}{R} \right) \\
& \Rightarrow 4M{{R}^{2}}{{\omega }_{f}}+4MRv=M{v}'+Mv \\
\end{align}\]
Substituting the given values in above equation we get:
\[\begin{align}
& 4\times \dfrac{5}{10}\times \dfrac{8}{10}{{\omega }_{f}}+4\times \dfrac{8}{10}\times 1={v}'+1 \\
& \Rightarrow {v}'={{\omega }_{f}}+1 \\
& \because 2R{{\omega }_{f}}+1={v}' \\
& \therefore {v}'\rangle {{\omega }_{f}}f \\
\end{align}\]
Therefore, we can say from the result that the friction between the ring and the ground is to the left.
Additional information:
As we know that, the friction force is defined as the force exerted by a surface as an object moves across it or makes an effort to move across it. There are mainly three types of friction forces: sliding friction, static friction and the last one rolling friction.
Static friction comes into action on objects when they are resting on a surface. For example, if we are hiking in the woods, there is a presence of static friction between our shoes and the trail each time we put down our foot. Without this friction, our feet would slip out and thereby, making it difficult to walk.
Sliding friction is friction that comes in action on objects when they are sliding over another surface. As we know that the sliding friction is weaker than the static friction. That is the reason that it is easier to slide a piece of furniture over the floor after we start it moving than it is to get it moving in the first place.
The last one is rolling friction is friction that comes in action on objects when they are rolling over another surface. Rolling friction is much weaker than sliding friction and static friction. This is the reason that most forms of ground transportation use wheels, including bicycles, cars, 4-wheelers, roller skates, scooters, and skateboards, as these wheels make it easier to travel with facing less frictional force.
Note:
Frictional force is a force that opposes the motion of any object. There are many practical examples of frictional force. We should also remember that various kinds of lubricants are used to overcome the frictional force like- grease, oil etc.
Recently Updated Pages
Mark and label the given geoinformation on the outline class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
When people say No pun intended what does that mea class 8 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Name the states which share their boundary with Indias class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give an account of the Northern Plains of India class 9 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Advantages and disadvantages of science
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Bimbisara was the founder of dynasty A Nanda B Haryanka class 6 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
10 examples of evaporation in daily life with explanations
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
How do you graph the function fx 4x class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)