Question

A pendulum having time period equal to two seconds is called a seconds pendulum. Those used in pendulum clocks are of this type. Find the length of a seconds pendulum at a place where g = π² m/s².

Answer 1

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Answer 2

In the question, They are talking about the second's pendulum.

Time period of second pendulum =  2 seconds.

acceleration due to gravity at a place = π² m/s²

Using the formula,

 $T = 2\pi \sqrt{\frac{l}{g} }$

where T is the time period, l is the length of the second pendulum and g is the acceleration due to gravity.

Note ⇒ g is  not the real acceleration due to gravity but it is the g effective. Thu you can't assume its value to be 9.8. It varies with place and motion. Now, it is given in the question as π² m/s². Thus, we need to put this only.

2 = 2π√(l/π²)

4 = 4π² × l/π²

4 = 4 × l

l = 1 m.

Hence, the length of the second pendulum should be 1 m.

Hope it helps.