In the question number 66, if wheel starts from rest, what is the kinetic energy of the wheel when 2 m of the cord is unwound?

In the question number 66, if wheel starts from rest, what is the kine

1.	In the question number 66, if wheel starts from rest, what is the kinetic energy of the wheel when 2 m of the cord is unwound?
Answer» 20 J 25 J 45 J 50 J Solution :Here, R=20 cm=0.2 m, M=20 KG As `tau=FR=(25)N(0.2)m = 5Nm` Moment of inertia of flywheel about its axis is `I=(MR^(2))/(2) = ((20kg)(0.2m)^(2))/(2) = 0.4 kg m^(2)` As `tau=Ialpha` `therefore` Angular accelerations of the WHEEL, `alpha=tau/I = (5Nm)/(0.4 kg m^(2))=12/5 rad s^(-2)` Angular displacement of wheel, `theta= ("LENGTH of unwound string")/("Radius of the wheel")= (2m)/(0.2m)=10 rad` LET `omega` be final angular velocity. As `omega^(2) = omega_(0)^(2)+2alphatheta` since, the wheel starts from rest, therefore `omega_(0)=0` `therefore omega^(2) = 2 x (12.5 rad s^(-2))(10 rad) = 250 rad^(2)s^(-2)` `therefore` Kinetic energy gained, `K=1/2Iomega^(2)` `K=1/2 xx 0.4 kg m^(2) xx 250 rad^(2)s^(-2)= 50J`