JEE Physics/ Lakshmikanta Satapathy/ Rigid body rotation QA part 3/ JEE main question on Motion of a block hanging from a string passing over a cylinder of finite mass solved with the related concepts

1. Physics Helpline
L K Satapathy Rigid Bodies QA 3
Motion of Pulley Block System
R
m
m

2. Physics Helpline
L K Satapathy Rigid Bodies QA 3
Question : A block of mass m is supported by a massless string
wound around a uniform hollow cylinder of mass m and radius R
as shown in the figure. The string does not slip on the cylinder.
The acceleration of the block when it is released from rest is
5 2
( ) ( ) ( ) ( )
6 3 2
g g g
a b g c d
R
m
m
Moment of Inertia a hollow cylinder of mass m and radius R is given by 2
I mR
If a torque  produces an angular acceleration  in it , then I 
Angular acceleration and linear acceleration are related as a
R
 
When a force F acts at perpendicular distance r from the axis , then F r 
Concepts :

3. Physics Helpline
L K Satapathy Rigid Bodies QA 3
Correct option = (d)
For the cylinder
2
(1)&(2) aTR I mR mRa
R
   
For the block ( ) . . . (4)mg T ma T m g a    
(3) & (4) ( )m g a ma  
Answer :
R

T
I
Let the tension in the string = T
 Clockwise torque on the cylinder is . . . (1)TR 
If angular acceleration of the cylinder =  , then . . . (2)I 
. . . (3)T ma 
mg
T
a
]
2
[
g
g a a a Ans    
R
m
m
T

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L K Satapathy
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