The document discusses a physics problem involving two blocks and a pulley system, providing equations related to their motions. It details the calculation of acceleration and torque, concluding that options (a) and (c) are correct regarding the system's behavior. The analysis emphasizes the relationship between linear and angular accelerations in non-slipping systems.

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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