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Answer:
0.0034 sec
Explanation:
L = initial length
T = initial time period = 2.51 s
Time period is given as
L = 1.56392 m
L' = new length
ΔT = Rise in temperature = 142 °C
α = coefficient of linear expansion = 19 x 10⁻⁶ °C
New length due to rise of temperature is given as
L' = L + LαΔT
L' = 1.56392 + (1.56392) (19 x 10⁻⁶) (142)
L' = 1.56814 m
T' = New time period
New time period is given as
T' = 2.5134 sec
Change in time period is given as
ΔT = T' - T
ΔT = 2.5134 - 2.51
ΔT = 0.0034 sec
To solve this problem we will derive the expression of the precession period from the moment of inertia of the given object. We will convert the units that are not in SI, and finally we will find the precession period with the variables found. Let's start defining the moment of inertia.
Here,
M = Mass
R = Radius of the hoop
The precession frequency is given as
Here,
M = Mass
g= Acceleration due to gravity
d = Distance of center of mass from pivot
I = Moment of inertia
= Angular velocity
Replacing the value for moment of inertia
The value for our angular velocity is not in SI, then
Replacing our values we have that
The precession frequency is
Therefore the precession period is 5.4s