Answer
397.8k+ views
Hint: The acceleration of the block is the same as the linear acceleration of the rim. The tension in the string is the driver of the rim.
Formula used: In this solution we will be using the following formulae;
\[s = ut + \dfrac{1}{2}a{t^2}\] where \[s\] is the distance covered by an accelerating body, \[u\] is the initial velocity, \[a\] is the acceleration of the body, and \[t\] is the time elapsed.
\[Fr = I\alpha \] where \[F\] is the force acting on a body, \[r\] is the distance of \[F\] from an axis of rotation, \[I\] is the moment of inertia of the body and \[\alpha \] is the angular acceleration. The quantity, \[Fr\] is the torque on a body.
\[\alpha = \dfrac{a}{r}\] where \[a\] is the linear acceleration, and \[r\] is the radius of a body.
Complete Step-by-Step solution:
Generally, moment of inertial and the force acting on a body are related through
\[Fr = I\alpha \] where \[F\] is the force acting on a body, \[r\] is the distance of \[F\] from an axis of rotation, \[I\] is the moment of inertia of the body and \[\alpha \] is the angular acceleration.
Hence, to find the moment of inertia, we need to know the force of the rim and the angular acceleration.
Angular acceleration is \[\alpha = \dfrac{a}{r}\] where \[a\] is the linear acceleration, and \[r\] is radius.
The acceleration can be gotten from
\[s = ut + \dfrac{1}{2}a{t^2}\] where \[s\] is the distance covered by an accelerating body, \[u\] is the initial velocity, \[a\] is the acceleration of the body, and \[t\] is the time elapsed.
Hence,
\[5 = \dfrac{1}{2}a{\left( 2 \right)^2}\]
\[ \Rightarrow a = \dfrac{5}{2}m/s\]
Then
\[\alpha = \dfrac{{\dfrac{5}{2}}}{{0.5}} = 5rad/{s^2}\]
The force driving the rim is the tension, hence to calculate tension on string, we perform newton's law analysis on block
\[mg - T = ma\]
\[ \Rightarrow 2\left( {10} \right) - T = 2\left( {\dfrac{5}{2}} \right)\]
Hence,
\[T = 15N\]
Then,
\[Tr = I\alpha \]
\[ \Rightarrow 15(0.5) = I\left( 5 \right)\]
Then by dividing both side by 5, we have
\[I = \dfrac{{15\left( {0.5} \right)}}{5} = 2.5kg{m^2}\]
Hence, the correct option is C
Note: For clarity, the tension is the force which drives the rim because the string is the object directly in contact with the rim. The tension is as a result of the block hanging down, however it’s not the weight that drives it but the transmitted force along the string (which is the tension).
Formula used: In this solution we will be using the following formulae;
\[s = ut + \dfrac{1}{2}a{t^2}\] where \[s\] is the distance covered by an accelerating body, \[u\] is the initial velocity, \[a\] is the acceleration of the body, and \[t\] is the time elapsed.
\[Fr = I\alpha \] where \[F\] is the force acting on a body, \[r\] is the distance of \[F\] from an axis of rotation, \[I\] is the moment of inertia of the body and \[\alpha \] is the angular acceleration. The quantity, \[Fr\] is the torque on a body.
\[\alpha = \dfrac{a}{r}\] where \[a\] is the linear acceleration, and \[r\] is the radius of a body.
Complete Step-by-Step solution:
Generally, moment of inertial and the force acting on a body are related through
\[Fr = I\alpha \] where \[F\] is the force acting on a body, \[r\] is the distance of \[F\] from an axis of rotation, \[I\] is the moment of inertia of the body and \[\alpha \] is the angular acceleration.
Hence, to find the moment of inertia, we need to know the force of the rim and the angular acceleration.
Angular acceleration is \[\alpha = \dfrac{a}{r}\] where \[a\] is the linear acceleration, and \[r\] is radius.
The acceleration can be gotten from
\[s = ut + \dfrac{1}{2}a{t^2}\] where \[s\] is the distance covered by an accelerating body, \[u\] is the initial velocity, \[a\] is the acceleration of the body, and \[t\] is the time elapsed.
Hence,
\[5 = \dfrac{1}{2}a{\left( 2 \right)^2}\]
\[ \Rightarrow a = \dfrac{5}{2}m/s\]
Then
\[\alpha = \dfrac{{\dfrac{5}{2}}}{{0.5}} = 5rad/{s^2}\]
The force driving the rim is the tension, hence to calculate tension on string, we perform newton's law analysis on block
\[mg - T = ma\]
\[ \Rightarrow 2\left( {10} \right) - T = 2\left( {\dfrac{5}{2}} \right)\]
Hence,
\[T = 15N\]
Then,
\[Tr = I\alpha \]
\[ \Rightarrow 15(0.5) = I\left( 5 \right)\]
Then by dividing both side by 5, we have
\[I = \dfrac{{15\left( {0.5} \right)}}{5} = 2.5kg{m^2}\]
Hence, the correct option is C
Note: For clarity, the tension is the force which drives the rim because the string is the object directly in contact with the rim. The tension is as a result of the block hanging down, however it’s not the weight that drives it but the transmitted force along the string (which is the tension).
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
Difference between Prokaryotic cell and Eukaryotic class 11 biology 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)
Fill the blanks with the suitable prepositions 1 The class 9 english 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)
Difference Between Plant Cell and Animal Cell
![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)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![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)