Answer:
Explanation:
The turntable that is rotating apparatus whose moment of inertia ( I ) is to be calculated is used as a spool of radius r. m mass is going down with acceleration a and rotating the apparatus with the help of cord with tension T wound around it
For motion of weight m
mg - T = ma
and for the motion of spool or apparatus
Tr = I a/r
T = Ia/r²
mg - Ia/r² = ma
mg = Ia/r² + ma
a ( I/r² + m ) = mg
When the counterweight m is released from rest it descends through a distance h, acquiring a speed v
v² = 2ah
a = v² / 2h
v² / 2h ( I/r² + m ) = mg
( I/r² + m ) = 2mgh / v²
I/r² = 2mgh / v²- m
I = r² (2mgh / v²- m )
= mr² ( 2gh/ v² -1 )
Proved .
