COMEDK 2024 Shift 1 Paper

To find the work done on the body, we need to understand the relationship between torque, angular acceleration, and work done in rotational motion.
We know the following:
Mass of the body, m=5‌kg
Time of rotation, t=25 s
Constant moment of force (torque), τ=10‌Nm
Moment of inertia, I=5‌kg‌m2
First, we find the angular acceleration. Torque (τ) is related to angular acceleration ( α ) by the equation:
τ=Iα

Solving for angular acceleration (α) :
α=‌

τ

I

=‌

10‌Nm

5‌kg‌m

=2‌rad∕ s2
Next, we need to find the final angular velocity (ω) after time t. The initial angular velocity (ω0) is zero because the body is at rest initially. Using the kinematic equation for rotational motion:
ω=ω0+αt
Substitute the known values:

ω=0+(2‌rad∕ s2)(25 s)=50‌rad∕ s
Now, we can calculate the work done. The work done by a torque in rotational motion is given by:
W=‌

1

2

Iω2
Substitute the known values:
W=‌

1

2

(5‌kg‌m2)(50‌rad∕ s)2
Calculate the work done:
W=‌

1

2

×5×(50)2=‌

1

2

×5×2500=6250J
The work done is 6250 J , which corresponds to Option C.