Answer
Verified
384.9k+ views
Hint: We need to understand the relation between the tension experienced by a string and the angular velocity of the string when it is rotated about a vertical axis in order to solve the angular velocity to get the solution for this problem.
Complete answer:
We are given a situation in which a ball is suspended on a string which is fixed at one end and hangs down which can be rotated about this fixed point on the vertical plane. The tension that can be afforded by the string is 324 N.
We know that the tension produced on the string is dependent on the mass of the ball, the angular velocity of the rotation and the radius of the rotation of the ball. The radius of the rotation is dependent on the angle subtended by the string with the vertical. It can be given as –
\[R=L\sin \theta \]
Where, L is the length of the string.
Now, we can find the maximum angular velocity that the string can afford using the relation between the tension and the angular momentum as –
\[\begin{align}
& T\sin \theta =m{{\omega }^{2}}R \\
& \Rightarrow T\sin \theta =m{{\omega }^{2}}L\sin \theta \\
& \Rightarrow T=m{{\omega }^{2}}L \\
& \Rightarrow \omega =\sqrt{\dfrac{T}{mL}} \\
& \Rightarrow \omega =\sqrt{\dfrac{324}{0.5\times 0.5}} \\
& \therefore \omega =36rad{{s}^{-1}} \\
\end{align}\]
So, the angular velocity which can be applied to the system such that the system is not destroyed is 36 radians per second.
The correct answer is option D.
Note:
We can see that the angular momentum which we equated to the tension is nothing but the force acting in the system due to the rotational torque. The force is dependent on the torque which is equivalent to the angular momentum in circular motion.
Complete answer:
We are given a situation in which a ball is suspended on a string which is fixed at one end and hangs down which can be rotated about this fixed point on the vertical plane. The tension that can be afforded by the string is 324 N.
We know that the tension produced on the string is dependent on the mass of the ball, the angular velocity of the rotation and the radius of the rotation of the ball. The radius of the rotation is dependent on the angle subtended by the string with the vertical. It can be given as –
\[R=L\sin \theta \]
Where, L is the length of the string.
Now, we can find the maximum angular velocity that the string can afford using the relation between the tension and the angular momentum as –
\[\begin{align}
& T\sin \theta =m{{\omega }^{2}}R \\
& \Rightarrow T\sin \theta =m{{\omega }^{2}}L\sin \theta \\
& \Rightarrow T=m{{\omega }^{2}}L \\
& \Rightarrow \omega =\sqrt{\dfrac{T}{mL}} \\
& \Rightarrow \omega =\sqrt{\dfrac{324}{0.5\times 0.5}} \\
& \therefore \omega =36rad{{s}^{-1}} \\
\end{align}\]
So, the angular velocity which can be applied to the system such that the system is not destroyed is 36 radians per second.
The correct answer is option D.
Note:
We can see that the angular momentum which we equated to the tension is nothing but the force acting in the system due to the rotational torque. The force is dependent on the torque which is equivalent to the angular momentum in circular motion.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Why Are Noble Gases NonReactive class 11 chemistry CBSE
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
Trending doubts
Guru Purnima speech in English in 100 words class 7 english CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Difference Between Plant Cell and Animal Cell
Change the following sentences into negative and interrogative class 10 english CBSE
Select the word that is correctly spelled a Twelveth class 10 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers