Question

please help..

need detailed answer.​

Answer 1

Question :

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

Theory :

•Second's Pendulum

If the Time period of a simple Pendulum is 2 seconds then it is called second's pendulum .

For second's Pendulum, time period

${\purple{\boxed{\large{\bold{t=2\pi\sqrt{\frac{l}{g}}}}}}}$

Solution ;

We know that ,

$t = 2\pi \sqrt{ \frac{l}{g} }$

$\implies \: t \propto \sqrt{l}$

Take log on both sides

$\implies \: log(t) = log(l) {}^{ \frac{1}{2} }$

$\implies \: \frac{ \triangle \: t }{t} = \frac{1}{2} \times \frac{ \triangle \: l }{l}$

$\implies \: \frac{ \triangle \: t}{t} \times 100 = \frac{ \triangle \: l}{l} \times 100 \: \: ...(1)$

★ According to the Question length is length decreased by 2%

$\implies \: \frac{ \triangle l }{l} = 0.02$

put this value in Equation (1)

________________________

$\frac{ \triangle \: t}{t} = \frac{1}{2} \times 0.02 \times 100$

$\implies \: \frac{ \bold\triangle \: t}{t} = 1\%$

Lost of time per day

= 0.01×24×60×60

= 864 seconds

Answer 2

Answer:

option c is the correct answer. It would lose 864 s in a day.