Answer
417.9k+ views
Hint The maximum tension in the string will be at the point when the maximum force is exerted on the stone that is tied at the end of the string. The tension will be a sum of the centrifugal force and the force due to gravitational acceleration.
Complete step by step answer
We’ve been given that a stone tied to the end of a string is being whirled in a vertical circle at a constant speed. The forces that will act on the stone will be due to the centrifugal force that will always be outwards away from the center of the string and the gravitational acceleration that is acting on the stone which is always downwards in nature.
Hence the tension in the string is
$\Rightarrow T = \dfrac{{m{v^2}}}{R} + mg\cos \theta $ where $R$ is the radius of the circle of the stone path, $v$ is its velocity, and $\theta $ is the angle of the line formed between the string and the vertical.
Substituting the value of $T = 52\,N$, $v = 4\,m/s$ and $R = 1\,m$, we get
$\Rightarrow 52 = \dfrac{{2{{(4)}^2}}}{1} + \left( {2 \times 10} \right)\cos \theta $
Subtracting both sides by 32, we get
$\Rightarrow 52 = 52\cos \theta $ which gives us
$\Rightarrow \cos \theta = 1$
$\therefore \theta = 0^\circ $
Hence the string will have a tension of 52 N when the stone is the lowest point in its circle which corresponds to option (B).
Note
We should be careful to give a direction to the gravitational acceleration since the tension will be in the direction of the string while the centrifugal force will always be directed outwards away from the centre of the circle and in the direction opposite to the tension and the gravitational force will always be downwards so we must take its component in the direction of the tension which depends on the angle formed by the string with the vertical.
Complete step by step answer
We’ve been given that a stone tied to the end of a string is being whirled in a vertical circle at a constant speed. The forces that will act on the stone will be due to the centrifugal force that will always be outwards away from the center of the string and the gravitational acceleration that is acting on the stone which is always downwards in nature.
Hence the tension in the string is
$\Rightarrow T = \dfrac{{m{v^2}}}{R} + mg\cos \theta $ where $R$ is the radius of the circle of the stone path, $v$ is its velocity, and $\theta $ is the angle of the line formed between the string and the vertical.
Substituting the value of $T = 52\,N$, $v = 4\,m/s$ and $R = 1\,m$, we get
$\Rightarrow 52 = \dfrac{{2{{(4)}^2}}}{1} + \left( {2 \times 10} \right)\cos \theta $
Subtracting both sides by 32, we get
$\Rightarrow 52 = 52\cos \theta $ which gives us
$\Rightarrow \cos \theta = 1$
$\therefore \theta = 0^\circ $
Hence the string will have a tension of 52 N when the stone is the lowest point in its circle which corresponds to option (B).
Note
We should be careful to give a direction to the gravitational acceleration since the tension will be in the direction of the string while the centrifugal force will always be directed outwards away from the centre of the circle and in the direction opposite to the tension and the gravitational force will always be downwards so we must take its component in the direction of the tension which depends on the angle formed by the string with the vertical.
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)