Question

30. (a) What is the effect on the period of a pendulum if you double its length?

(b) What is the effect on the period of a pendulum if you decrease its length by 5.00%?

The answers are "(a) Period increases by a factor of 1.41 (2–√)(b) Period decreases to 97.5% of old period" but please include all of your work.

Answer 1

Let's know the formula

`\\ \rm\rightarrowtail T=2\pi \sqrt{(l)/(g)}`

So

`\\ \rm\rightarrowtail T\propto √(l)`

Hence if length is doubled time period will be √2 times

• √2=1.41 (Approximately)

#2

Decrease by 5% will decrease the time period 5/2=2.5%

So

It's

• 100-2.5=97.5% of old period