AP EAPCET 23-Aug-2021 Shift 2 Paper

Given, mass of disc, M=4‌kg
Radius of disc, R=0.4m
Initial angular velocity of disc, ω1=30‌rad‌s−1
Mass of point-masses, m=0.25‌kg
Now, moment of inertia of disc, I3=

1

2

MR2
Moment of inertia of disc and two point mass system,
I2=

1

2

MR2+2mR2
Let ω2 be the final angular velocity.
According to conservation of angular momentum,
I1ω1=I2ω2⇒ω2=

I1ω1

I2

Substituting the values, we get
ω2=

1 2 MR2(30)

( 1 2 MR2+2mR2)

=

1 2 ×4×(0.4)2×30

1 2 ×4×(0.4)2+2×0.25×(0.4)2

ω2=24‌rad∕s
Hence, the final angular velocity of system is 24‌rad∕s.