Answer:
0.010 m
Explanation:
So the equation for a pendulum period is:
where L is the length of the pendulum. In this case I'll use the approximation of pi as 3.14, and g=9.8 m\s. So given that it oscillates once every 1.99 seconds. you have the equation:

Evaluate the multiplication in front

Divide both sides by 6.28

Square both sides

Multiply both sides by m/s^2 (the s^2 will cancel out)
Now now let's find the length when it's two seconds

Divide both sides by 6.28

Square both sides

Multiply both sides by 9.8 m/s^2 (s^2 will cancel out)

So to find the difference you simply subtract
0.984 - 0.994 = 0.010 m
Answer:
ωf = 0.16 rad/s
Explanation:
Moment of inertia of the child = mr² = 20(1.6²) = 51.2 kg•m²
Moment of Inertia of the MGR = ½mr² = ½(180)1.6² = 230.4 kg•m²
(ASSUMING it is a uniform disk)
Initial angular momentum of the child = Iω = I(v/r) = 51.2(1.4/1.6) = 44.8 kg•m²/s
Conservation of angular momentum
44.8 = (51.2 + 230.4)ωf
ωf = 0.15909090...