Step 1: Pendulum Frequency Formula
The time it takes for one swing (period) of a simple pendulum is given by
T=2π√, where
l is length and
g is gravity.
Frequency (
f ) is how many swings it makes in one second, so
f==√.
Step 2: Relationship Between Frequency and Length
From this, frequency is inversely related to the square root of length:
f∝.
This means
=√, where
l1 and
f1 are initial length and frequency, and
l2 and
f2 are final.
Step 3: Assign the Values
The number of swings in a minute is frequency per minute. Original frequency
=72, new frequency
=90.
So,
==.
Now,
=√.
Step 4: Find the New Length
Square both sides:
()2=, so
=.
Rearrange to get
l2=l1.
Step 5: Calculate the Percentage Decreased
Decrease in length
=l1−l2.
Percentage decrease
=×100%.
Substituting values:
×100%=×100%=36%.
