Two simple pendulum A and B of length 1.69 m and 1.44 m start swinging at the same
time from a location where acceleration due to gravity is 10 ms2.-
Answer the following questions
1.
How many vibrations pendulum A will complete when it will be out of phase
with B?
(a) 4
(b) 5
(c) 6
(d) 8
2.
After how much time, the two pendulums will be out of phase?
(a) 5.5 s
(b) 10,0 s
(C) 12.6
(d) 15.5
3.After how much time, the two pendulums will be in phase again?
(a) 11.0 s
(b) 20.0
(C) 25.2 s
(d) 31.0 s
4.What will be the approximate gain or loss of time by pendulum A in day with
respect to second's pendulum?
(a) 6 hours
(b) 7 hours
(C) 8 hours
(d) 9 hours
Answers
Given : Two simple pendulum A and B of length 1.69 m and 1.44 m start swinging at the same
time from a location where acceleration due to gravity is 10 m/s²
To Find : How many vibrations pendulum A will complete when it will be out of phase with B?
After how much time, the two pendulums will be out of phase?
After how much time, the two pendulums will be in phase again
.What will be the approximate gain or loss of time by pendulum A in day with respect to second's pendulum
Solution:
T = 2π √L/g
=> T = 2π √1.69/10 = 2.583 sec
T = 2π √1.44/10 = 2.384 sec
2.384 * (n + 1) = 2.583 * n
=> n = 12
Hence after 12 complete rounds of 2.583 pendulum A
or 13 complete rounds of 2.384 pendulum B
they will be in phase again
2.583 * 12 = 2.384 * 13 = 31
=> 31 sec
Hence they will be out of phase in 31/2 = 15.5 secs and after 6 rounds of pendulum A
approximate gain or loss of time by pendulum A in day with
respect to second's pendulum
second's pendulum time period = 2 secs
Pendulum A losses 2.583 - 2 = 0.583 sec for every 2 secs
Hence (0.583/ 2 ) * 24 = 7 hrs
Hence approximate loss of time by pendulum A in day with
respect to second's pendulum
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