Question

a pendulum of length 1m has a time period of 2s.Calculate the time period if the length is reduced to half

Answer 1

Given :

Time period = 2 s

Length = 1 m .

We know that :

$\mathsf{T=2\pi \sqrt{\frac{l}{g}}}$

Hence time period is directly proportional to the square root of the length .

If length is reduced to half , then the distance will be reduced to square root of half .

Time period = 2 s

2 s will be become $\frac{2}{\sqrt{2}}$

                            =  $\frac{2\sqrt{2}}{2}$

                            = $\sqrt{2}$

The time period will be $\sqrt{2}s$