Question

How will the time period of a simple pendulum change if its length is doubled?

Answer 1

T=2π√(l/g).......(I) T¹=2π(2l/g).........(II) I÷|| T/T¹=√1/2 T¹=T√2

Answer 2

⇒ T = 2π√l/g

⇒ T² = 4π² ( l/g)

All are constants ,

⇒ T² ∝ l

= T = √kl , k be any proportionality constant

Now , if length is doubled ,

⇒ T² ∝ 2l

⇒ T = k √2l

So time period will increase by √2 times