Two masses 
and 2 m are connected by a light string going over a pulley (disc) of mass 30 m with radius 
. The pulley is mounted in a vertical plane and it is free to rotate about its axis. The 2 m mass is released from rest and its speed when it has descended through a height of 3.6 m is 
m/s. (Assume string does not slip and 
)
Text Solution
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(2) Let the speed of the masses be 
and the angular velocity of the pulley be 
since the string does not slip.
The pulley is a disc of mass 
and radius 
. Its moment of inertia is 
.
Using the principle of conservation of mechanical energy, the loss in potential energy of the system equals the gain in kinetic energy.
When the mass 
descends by 
, the mass 
ascends by 
.
Loss in potential energy 
.
Gain in kinetic energy 
.
Substituting 
and 
: 
.
Equating 
.
.
Given 
and 
:
.
.
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