Question

What is the effect on the period of a pendulum if you decrease its length by 7.85%? (Answer this question in terms of the initial period T.)

Answer 1

Answer:

0.955T

Explanation:

The effect on the period in case when there is a decrease in length by 7.85%

Let us assume the following items

Period = T

T= Beginning period

L = Beginning length

T' = Final period

L' = Final length

Based on the above information

As we know that

$\frac {T'}{T} = \sqrt {\frac {L'}{L}}\\\\ L' = \frac {100-7.85}{100} \\\\ L = 0.9215 \: L$

Therefore

$\frac {T'}{T} = \sqrt {\frac {0.9215L}{L}} \\\\= 0.955\ T$

Hence, the effect on the period is 0.955T