Answer:
length L of the clapper rod for the bell to ring silently = 0.756m
Explanation:
We are given;
Mass of Bell;m_b = 34 kg
Distance of centre of mass from pivot;d = 0.7m
The bells moment of inertia about an axis at the pivot;I = 18 kg.m²
Mass of clapper;m_c = 1.8 kg
Length of slender rod is L
Now, the formula for period of physical pendulum having small amplitude is given as;
T_b = 2π√(I/mgd)
Where;
I is moment of inertia
m is mass
g is acceleration due to gravity = 9.8 m/s²
d is distance from rotation axis to centre of gravity
Plugging in the relevant values and using mass of bell, we have;
T_b = 2π√(18/(34*9.81*0.7)
T_b = 2π√(18/(34*9.81*0.7)
T_b = 1.745 s
Now, the formula for period for a simple pendulum which is essentially what the clapper rod is would be;
T_c = 2π√(L/g)
Now, we want to find length of clapper L.
Thus, let's make it the subject;
L = g(T_c/2π)²
Now, we are told that for the bell to ring silently, T_b = T_c.
Thus, T_c = 1.745 s.
So,
L = 9.8(1.745/2π)²
L = 0.756m
