TG EAMCET 3 May 2025 Shift 2 Paper

Step 1: Pendulum Frequency Formula
The time it takes for one swing (period) of a simple pendulum is given by T=2π√‌

l

g

, where l is length and g is gravity.
Frequency ( f ) is how many swings it makes in one second, so f=‌

1

T

=‌

1

2π

√‌

g

l

.
Step 2: Relationship Between Frequency and Length
From this, frequency is inversely related to the square root of length: f∝‌

1

√l

.
This means ‌

f2

f1

=√‌

l1

l2

, 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, ‌

f2

f1

=‌

90

72

=‌

5

4

.
Now, ‌

5

4

=√‌

l1

l2

.
Step 4: Find the New Length
Square both sides: (‌

5

4

)2=‌

l1

l2

, so ‌

25

16

=‌

l1

l2

.
Rearrange to get l2=‌

16

25

l1.
Step 5: Calculate the Percentage Decreased
Decrease in length =l1−l2.
Percentage decrease =‌

l1−l2

l1

×100%.
Substituting values: ‌

l1− 16 25 l1

l1

×100%=‌

9

25

×100%=36%.