Physics
posted by James on .
10. A yoyo is made by wrapping a 2m long string around a 500g 10cm diameter uniform disk. The string is fastened to the ceiling, and the yoyo is released. What is the tension in the string as the yoyo falls?
A.9.8N
B.1.6N
C.4.9N
D. 0.49N
E.3.3N
The answer is B. How do I get this answer? I'm having trouble figuring out why tension would be less than (mg). Thank you in advance.

Tension = T
force up = T
force down = m g
m g  T = m a
torque = I * angular acceleration
T * R = I alpha = I a/R
but I for disk = (1/2) m R^2
so
T R = (1/2) m R a
T = (1/2) m a interesting :)
so
m g  (1/2) m a = m a
g = (3/2) a
a = (2/3) g
so
T = (1/2) m (2/3) g = (1/3) m g
= (1/3)(0.5)(9.81)
= 1.63 N or B 
Ttension, M –torque,
I = mR²/2 moment of inertia of disc
εangular acceleration
T•R= M
I•ε =M
ε =a/R
I•a/R = T•R,
a=TR²/I= 2TR²/mR²=2T/m,
ma=mgT
m•2T/m = mgT,
T=mg/3 =0.5•9.8/3 = 1.63
ANS: B