Question

the length of the pendulum is increased by 45%. the % increase in the time period will consequently be spproximately a)55%b)20%c)root45%d)root55%​

Answer 1

$\Large\underline{\underline{\sf Given:}}$

• Lenght of pendulum is increased by 45%

$\Large\underline{\underline{\sf To\:Find:}}$

• Increase in time period .

$\Large\underline{\underline{\sf Formula\:Used:}}$

$\large{\boxed{\boxed{\sf \pink{T=2π\sqrt{\dfrac{l}{g}}}}}}$

$\Large\underline{\underline{\sf Solution:}}$

Let the initial Lenght be l

When 44% of Lenght is increased then ,

New Lenght = l + 0.44l

⠀⠀⠀⠀⠀⠀⠀⠀= 1.44l

New Time period (T')

$\large{\boxed{\sf T=2π\sqrt{\dfrac{l}{g}}}}$

$\implies{\sf T'=2π\sqrt{\dfrac{1.44l}{g}}}$

$\implies{\sf T'=1.2×2π\sqrt{\dfrac{l}{g}}}$

$\implies{\sf T'=1.2T }$

•°• Time period is increased by 20%

$\Large\underline{\underline{\sf Answer:}}$

Option (b) 20%