Question

Question #d5bf8

Answer 1

The period will increase by `0.5%`

The period `T` for small start-angles is given by:

`T=2pi*root 2 (l/g)=((2pi)/root 2 g)*root 2 l =2.006.root 2 l`
Where `l`=length (in m), `g`=acceleration of gravity (`9.81 m//s^2`)

Conclusion
The period is in direct ratio to the square root of the length.
The ratio is 2.006

Calculation
A length increase of 1% means an increase by a factor of `1.01`

The period will increase by a factor of `root 2 1.01=1.004999`

This means an increase of `0.5%` (very slightly rounded)

Extra
For small length changes you may use the rule of thumb that a percentage change in length will give about half the percentage change in period. (a 10% length change will add 4.9% to the period - you decide whether that's acceptable, or you can use the formula).