Question

Given below are two statements: Statement (1):- A second’s pendulum has a time period of 1 second. Statement (2):- It takes precisely one second to move between the two extreme positions
In light of the above statements, choose the correct answer from the options given below.
A. Both Statement I and Statement II are false
B. Statement I is true but Statement II is false
C. Statement I is false but Statement II is true
D. Both Statement I and Statement II is true

Answer 1

Hint: A Pendulum which has a frequency of 0.5 Hz is called a second’s pendulum. The time period of a second’s pendulum is 2 seconds. It takes 1 second to swing in one direction and another second to swing in the opposite direction.



Formula used:
Time period of a second’s pendulum= 2sec
Time which a particle takes while performing SHM (Simple Harmonic Motion) between two extreme points \[\dfrac{T}{2} = \]\[\dfrac{2}{2}\] = 1sec



Complete answer:
The first statement states that the time period of a second’s pendulum is 1sec. Since the time period of a second's pendulum is 2 seconds, the first statement is incorrect.

The second statement states that the time taken by a particle to move between two extreme positions is 1sec. As per the formula mentioned above and inferring from the basic concepts of second’s pendulum a particle performing simple harmonic motion takes 1 sec to move between one extreme to the other. Hence, this statement is correct.

Option cC is the correct answer.

Additional Information:
Basics of Pendulum Physics When a weight is suspended from a pivot so that it is allowed to move freely then it is called a Pendulum. When the weight is displaced from the position of rest (equilibrium position) a restoring force due to gravity acts on the weight and it tends to move back towards the equilibrium position. When the weight is released, the pendulum’s mass in combination with the restoring force causes it to swing back and forth about the equilibrium position..

Note:
Whenever you are solving this type of problem, always pay attention to the concept of time period. It is noted that the time period of the second pendulum is to complete one oscillation in 2 seconds. You can also calculate the length of the second pendulum by using its time period formula.