KCET 2025 Physics Paper

The relationship between the torque, moment of inertia, and angular acceleration for each wheel can be established with the following equations:
For the smaller wheel:
T1=I1α1
where T1 is the torque applied to the smaller wheel, I1=4‌kg⋅m2 is its moment of inertia, and α1 is the angular acceleration.
The angular acceleration ratio between the two wheels is given by:
α2r2=α1r1
where α2 is the angular acceleration of the larger wheel, r1=0.2m, and r2=0.3m.
Given that a torque of 10 Nm is applied to the smaller wheel:
10=α1×4
Solving for α1 :
α1=‌

10

4

=‌

5

2

‌rad∕ s2
Using the relation for the angular accelerations:
‌α2×0.3=(‌

5

2

)×0.2
‌α2=‌

5

3

‌rad∕ s2
Finally, for the larger wheel, the torque T2 is given by:
T2=I2α2
where I2=20‌kg⋅m2. Plugging in the values:
T2=20×‌

5

3

=‌

100

3

‌Nm
Thus, the angular accelerations and the torque can be summarized as follows:
Angular acceleration of the smaller wheel α1=‌

5

2

‌rad∕ s2
Angular acceleration of the larger wheel α2=‌

5

3

‌rad∕ s2
Torque on the larger wheel T2=‌

100

3

‌Nm