A pendulum is composed of a mass of 2.00 kg suspended from the ceiling by a string.The pendulum makes 1000 complete oscillations in an hour.What is the length of the string in m?
A)2.11
B)2.94
C)3.22
D)4.31
E)6.62

Question

A pendulum is composed of a mass of 2.00 kg suspended from the ceiling by a string.The pendulum makes 1000 complete oscillations in an hour.What is the length of the string in m? 
A)2.11 
B)2.94 
C)3.22 
D)4.31 
E)6.62

Quizplus · Accepted Answer

We know that the time period of a pendulum (T) is given by:

T = 2π√(l/g)

where l is the length of the pendulum and g is the acceleration due to gravity (9.81 m/s^2).

We can find the time taken by the pendulum to complete one oscillation (T_1) by dividing one hour (3600 seconds) by the number of oscillations made in one hour:

T_1 = 3600/1000 = 3.6 s

Now we can use the time period to find the length of the pendulum:

T = 2π√(l/g)

3.6 = 2π√(l/9.81)

Squaring both sides:

12.96 = 4π^2(l/9.81)

Multiplying both sides by 9.81/4π^2:

3.22 = l

Therefore, the length of the pendulum is 3.22 m, which is closest to choice C (3.22).

A Pendulum Is Composed of a Mass of 2