Answer:
The loss of initial Kinetic energy = 37.88 %
Explanation:
Given:
Rotational inertia of the turntable = 
Rotational inertia (
) of the record = 
According to the question:
<em>Frictional forces act to bring the record and turntable to a common angular speed.</em>
So,angular momentum will be conserved as it is an inelastic collision.
Considering the initial and final angular velocity of the turn table as
respectively.
Note :
Angular momentum
= Product of moment of inertia
and angular velocity
.
Lets say,
⇒ initial angular momentum = final angular momentum
⇒
⇒
⇒
...equation (i)
Now we will find the ratio of the Kinetic energies.
⇒
⇒ 
Their ratios:
⇒
⇒ 
Plugging the values of
as
from equation (i) in the ratios of the Kinetic energies.
⇒ 
Now,
The Kinetic energy lost in fraction can be written as:
⇒
Now re-arranging the terms.

Plugging the values of
and
.
⇒ 
To find the percentage we have to multiply it with
and here negative means for loss of Kinetic energy.
⇒ 
So the percentage of the initial Kinetic energy lost is 37.88