Concept explainers
(a)
The distance
(a)
Explanation of Solution
Given:
The length of rod is
The mass of rod is
The mass of uniform disk is
The radius of uniform disk is
The perfect time period of pendulum is
The actual time period of pendulum is
Formula used:
Write the expression for moment of inertia of rod passing through center of mass.
Here,
Write the expression for moment of inertia of disk passing through center of mass.
Here,
Write the expression for moment of inertia of system using parallel axis theorem.
Here,
The moment of inertia of system passing through center of mass is the sum of moment of inertia of rod and moment of inertia disk passing through center of mass.
Substitute
Write the expression for center of mass of system.
Here,
Write the expression for object in term of period of pendulum.
Here,
Rearrange the above expression in term of
Calculation:
Substitute
Substitute
Substitute
Conclusion:
Thus, the distance
(b)
The change in distance and direction of disk to keep the clock at perfect time period.
(b)
Explanation of Solution
Given:
The length of rod is
The mass of rod is
The mass of uniform disk is
The radius of uniform disk is
The perfect time period of pendulum is
The delay in time period of clock is
Formula used:
Write the expression for moment of inertia of rod passing through center of mass.
Here,
Write the expression for moment of inertia of disk passing through center of mass.
Here,
Write the expression for moment of inertia of system using parallel axis theorem.
Here,
The moment of inertia of system passing through center of mass is the sum of moment of inertia of rod and moment of inertia disk passing through center of mass.
Substitute
Write the expression for center of mass of system.
Here,
Write the expression for object in term of period of pendulum.
Here,
Rearrange the above expression in term of
Calculation:
Substitute
Substitute
Substitute
The clock loses
Calculate the time period of clock.
Substitute
Calculate the change in distance of disk.
Conclusion:
Thus, the disk will be moved upward by
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Chapter 14 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
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