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=5‌kgTime of rotation,
t=25 sConstant moment of force (torque),
τ=10‌NmMoment of inertia,
I=5‌kg‌m2First, we find the angular acceleration. Torque
(Ï„) is related to angular acceleration (
α ) by the equation:
τ=Iα Solving for angular acceleration
(α) :
α=‌=‌=2‌rad∕ s2Next, 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+αtSubstitute the known values:
ω=0+(2‌rad∕ s2)(25 s)=50‌rad∕ sNow, we can calculate the work done. The work done by a torque in rotational motion is given by:
W=‌Iω2Substitute the known values:
W=‌(5‌kg‌m2)(50‌rad∕ s)2Calculate the work done:
W=‌×5×(50)2=‌×5×2500=6250JThe work done is 6250 J , which corresponds to Option C.