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A grandfather clock has a pendulum that consists of a thin brass disk of radius r = 15.29 cm and mass 0.8709 kg that is attached to a long thin rod of negligible mass. The pendulum swings freely about an axis perpendicular to the rod and through the end of the rod opposite the disk, as shown in the figure. If the pendulum is to have a period of 2.441 s for small oscillations at a place where g = 9.848 m/s 2 , what must be the rod length L ?

A grandfather clock has a pendulum that consists of a thin brass disk of radius r = 15.29 cm and mass 0.8709 kg that is attached to a long thin rod of negligible mass. The pendulum swings freely about an axis perpendicular to the rod and through the end of the rod opposite the disk, as shown in the figure. If the pendulum is to have a period of 2.441 s for small oscillations at a place where g= 9.848 m/s2, what must be the rod length L?
 

Grade:12th pass

1 Answers

Arun
25750 Points
5 years ago
The period of a pendulum is given by: 
T = 2π √( L / g ) 
so 
L = g × (T / 2π)² 
where 
T = period = 2.441 s 
L = distance between axis and center of the disk 
g = acceleration by gravity =9.848 m/s² 
 
Now yoi can solve
 

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