JEE Physics/ Lakshmikanta Satapathy/ Rotational Motion QA part 8/ Question on Motion of a pulley block system having finite mass and moment of inertia

1. Physics Helpline
L K Satapathy
MCQ / One or More Correct
Rotational Motion QA 8
m1m2
m
AB
P
T1T2
aa

2. Physics Helpline
L K Satapathy Rotational Motion QA 8
Question : Two blocks A and B of masses m1 = 3kg and m2 = 1kg
are attached to the two ends of a string which passes over a
pulley P of mass m = 2kg and radius R = 0.5m as shown in
the figure . The string does not slip over the pulley. The system
is released from rest. If , then
(a) Acceleration of the system is 4 m/s2
(b) Acceleration of the system is 5 m/s2
(c) Torque on the pulley is 2 Nm
(d) Torque on the pulley is 4 Nm
Analysis :
2
10g m s
m1m2
m
AB
P
Block A will move down and block B will move up with the same acceleration.
Moment of Inertia of the pulley is finite & it will rotate with clockwise angular
acceleration. This needs a non-zero clockwise torque. Hence tensions in the string
on either side of the pulley are not equal. For clockwise torque , tension in the
right part of the string is greater than that on the left.

3. Physics Helpline
L K Satapathy
Answer :
2 10T a  
130 3T a  
1 2(1) & (2) 20 4 . . . (3)T T a   
Rotational Motion QA 8
Let the acceleration of the system = a
Given : 2
1 23 , 1 , 2 , 0.5 , 10m kg m kg m kg R m g m s    
For block A : 1 1 1m g T m a 
For block B : 2 2 2T m g m a 
1 30 3 . . . (1)T a   m1g
A
T1
a
m1m2
m
AB
P
T1T2
aa
2 10 . . . (2)T a   m2g
B
T2
a

4. Physics Helpline
L K Satapathy
1 2 1 2( ) . . . (4)T T R     
Rotational Motion QA 8
m
T1
T2
For the pulley :
Moment of Inertia 21
2
I mR
Clockwise torque due to T1 : 1 1T R 
2 2T R 
 Net clockwise torque
& anticlock torque due to T2 :
The pulley has clockwise angular acceleration
 The net torque on the pulley should be clockwise
1 2 1 2T T    
 Clockwise torque > Anticlock torque

5. Physics Helpline
L K Satapathy
21 1
. . . (5)
2 2
a
I mR mRa
R
    
1 2
1
(4) & (5) ( )
2
T T R mRa  
2
(3) & (6) 20 4 5 0 ]2 [4a a a a s Ansm      
1 2(4)& (6) ( ) [ ]4 0.5 2 AnsT T R aR Nm      
Rotational Motion QA 8
m
T1
T2
Again
 1 2
1
. . . (6)
2
T T ma a   
[  (a) is correct ]
[  (c) is correct ]
Correct options = (a) , (c)
For no slipping , Linear acceleration
& angular acceleration are related as
a
R
 
[ m = 2kg ]

6. Physics Helpline
L K Satapathy
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