Question

If the length of second's pendulum is decreased by 2%, how many seconds it will lose per day

Answer 1

$\huge\underline{\underline{\bf \orange{Question-}}}$

If the length of second's pendulum is decreased by 2%, how many seconds it will lose per day

$\huge\underline{\underline{\bf \orange{Solution-}}}$

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

• Length of second's pendulum is decreased by 2%

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

• How many seconds it will lose per day

❏$\large{\boxed{\bf \blue{T=2π\dfrac{l}{g}}}}$

i.e ${\sf \red{T \:\:\: \alpha \:\:\: \sqrt{l}}}$

$\implies{\sf T \:\:\alpha\:\:l^{1/2} }$

$\implies{\sf \dfrac{\triangle T}{T}=\dfrac{1}{2}\dfrac{\triangle l}{l} }$

$\implies{\sf \dfrac{\triangle l}{l}=2\%}$

$\implies{\sf \pink{\dfrac{\triangle l}{l}=0.02} }$

$\implies{\sf \dfrac{\triangle T}{T}=\dfrac{1}{2}×0.02 }$

$\implies{\sf \dfrac{\triangle T}{T}=0.01 }$

$\implies{\sf \triangle T=0.01T }$

Loss of time per day ➝

$\implies{\sf \triangle T = 0.01×24×60×60 }$

$\implies{\bf \red{\triangle T=864\:sec}}$

$\huge\underline{\underline{\bf \orange{Answer}}}$

Loss of time per day will be ${\bf \red{864\:sec}}$.