Answer:
Original length = 2.97 m
Explanation:
Let the original length of the pendulum be 'L' m
Given:
Acceleration due to gravity (g) = 9.8 m/s²
Original time period of the pendulum (T) = 3.45 s
Now, the length is shortened by 1.0 m. So, the new length is 1 m less than the original length.
New length of the pendulum is,
New time period of the pendulum is,
We know that, the time period of a simple pendulum of length 'L' is given as:
-------------- (1)
So, for the new length, the time period is given as:
------------ (2)
Squaring both the equations and then dividing them, we get:
Now, plug in the given values and calculate 'L'. This gives,
Therefore, the original length of the simple pendulum is 2.97 m