Question

The bob of a simple pendulum takes a totat time of 1.5 s to go trom B to A and then from A to O as shown. Then


(1) it will complete 20 oscillations in 40s
(2) it will complete 20 oscillations in 20s
(3) it will complete 50 oscillations in 75s
(4) it will complote 50 osciallations in 100s​

Answer 1

The of a simple pendulum takes a totat time of 1.5 s to go trom B to A and then from A to O as shown in figure then,

1. it will complete 20 oscillations in 40s
2. it will complete 20 oscillations in 20s
3. it will complete 50 oscillations in 75s
4. it will complote 50 osciallations in 100s​

from figure,

The bob completes an oscillation when it moves from O to B then returns B to O and then moves from O to A then finally returns A to O.

therefore, one complete oscillation = 2(time taken from A to O) + 2(time taken from B to O)

but here, time taken from A to O = time taken from B to O

so, one complete oscillation = 4( time taken from B to O) = 4 ( time taken from A to O) ....(1)

A/c to question, The bob takes the total time of 1.5sec to go from B to A and then from A to O.

⇒ 1.5 sec = time taken from B to A + time taken from A to O

⇒ 1.5 sec = (time taken from B to O + time taken from O to A) + time taken from A to O

⇒ 1.5 sec = 3(time taken from A to O)

⇒ 0.5 sec = time taken from A to O.

from equation (1) we get, time taken to complete one oscillation = 4 × 0.5 = 2sec

∴ it will complete 20 oscillations in 40s. and 50 oscillations in 100s.

Therefore the correct options are (1) and (4).