TG EAMCET 3 May 2025 Shift 1 Paper

Step 1: Find the moment of inertia of the disc.
The moment of inertia ( I ) for a disc about its center is I=‌

1

2

MR2
Here, the mass M=‌

10

π2

kg, and the radius R=2m.
So, I=‌

1

2

×‌

10

π2

×(2)2=‌

1

2

×‌

10

π2

×4=‌

20

π2

kgm2
Step 2: Change revolutions per minute (rev/min) to angular speed (rad/s).
The first speed is 90rev∕min. To convert to radians per second:
w1=90×‌

2π

60

=3πrad∕s
The second speed is 120rev∕min:w2=120×‌

2π

60

=4πrad∕s
Step 3: Use the rotational kinetic energy formula to find work done.
The work done to increase speed equals the change in rotational kinetic energy: Work Done =∆KE=‌

1

2

I(w22−w12)
Plug in the values: Work =‌

1

2

×‌

20

π2

[(4π)2−(3π)2]
Calculate:
‌(4π)2=16π2
‌(3π)2=9π2
So, 16π2−9π2=7π2
Therefore, Work =‌

1

2

×‌

20

π2

×7π2=10×7=70J