Answer
409.8k+ views
Hint: In this solution, we will first calculate the tension in the string on the left side and below the pulley. Then we will use the relation of torque and angular acceleration to determine the acceleration of the hanging mass.
Formula used: In this solution, we will use the following formula:
Torque of the pulley: $ \tau = F.r = I.\alpha $ where $ F $ is the force on the pulley, $ r $ is the radius of the pulley, $ I $ is the moment of inertia of the rod, and $ \alpha $ is the angular acceleration of the pulley.
Complete step by step answer
In the diagram given to us, the block on the flat surface will move to the right since there is no friction and the string will rotate over the pulley.
Let the tension in the string on the left of the pulley will be $ {T_1} $ and the tension in the string below the pulley be $ {T_2} $ and the acceleration of both the masses be $ a $ . The equation of motion of the top mass will be
$ {T_1} = ma $
And for the lower mass which is falling down will be
$ Mg - {T_2} = Ma $
Hence the force acting on the pulley will be
$ F = {T_2} - {T_1} $
The torque acting on the pulley will be determined from $ \tau = F.r = I.\alpha $ as
$ ({T_2} - {T_1})r = I\alpha $
Now, as $ \alpha = a/r $ , we have
$ ({T_2} - {T_1})r = \dfrac{{Ia}}{r} $
Substituting the values of $ {T_1} $ and $ {T_2} $ , we get
$ mg - 2ma = \dfrac{{Ia}}{{{r^2}}} $
Solving for $ a $ , we get
$ a = \dfrac{{mg}}{{2m + \dfrac{I}{{{r^2}}}}} $ which corresponds to option (A).
Note
Here we must realize that the acceleration of the two blocks will be the same since they are connected by a string. Also, the tension on two sides of the pulley will be unequal since the string will be rotating on the pulley without slipping.
Formula used: In this solution, we will use the following formula:
Torque of the pulley: $ \tau = F.r = I.\alpha $ where $ F $ is the force on the pulley, $ r $ is the radius of the pulley, $ I $ is the moment of inertia of the rod, and $ \alpha $ is the angular acceleration of the pulley.
Complete step by step answer
In the diagram given to us, the block on the flat surface will move to the right since there is no friction and the string will rotate over the pulley.
Let the tension in the string on the left of the pulley will be $ {T_1} $ and the tension in the string below the pulley be $ {T_2} $ and the acceleration of both the masses be $ a $ . The equation of motion of the top mass will be
$ {T_1} = ma $
And for the lower mass which is falling down will be
$ Mg - {T_2} = Ma $
Hence the force acting on the pulley will be
$ F = {T_2} - {T_1} $
The torque acting on the pulley will be determined from $ \tau = F.r = I.\alpha $ as
$ ({T_2} - {T_1})r = I\alpha $
Now, as $ \alpha = a/r $ , we have
$ ({T_2} - {T_1})r = \dfrac{{Ia}}{r} $
Substituting the values of $ {T_1} $ and $ {T_2} $ , we get
$ mg - 2ma = \dfrac{{Ia}}{{{r^2}}} $
Solving for $ a $ , we get
$ a = \dfrac{{mg}}{{2m + \dfrac{I}{{{r^2}}}}} $ which corresponds to option (A).
Note
Here we must realize that the acceleration of the two blocks will be the same since they are connected by a string. Also, the tension on two sides of the pulley will be unequal since the string will be rotating on the pulley without slipping.
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)