The length of a seconds pendulum at a place is 1.02m. Find the time period of another pendulum of length 0.51m at the same place.

The length of a seconds pendulum at a place is 1.02m. Find the time pe

1.	The length of a seconds pendulum at a place is 1.02m. Find the time period of another pendulum of length 0.51m at the same place.
Answer» <html><body><p></p>Solution :The <a href="https://interviewquestions.tuteehub.com/tag/time-19467" style="font-weight:bold;" target="_blank" title="Click to know more about TIME">TIME</a> period of a <a href="https://interviewquestions.tuteehub.com/tag/simple-1208262" style="font-weight:bold;" target="_blank" title="Click to know more about SIMPLE">SIMPLE</a> pendulum is `T=2pisqrt((l)/(g))`………….(1) <br/> i.e., `(l)/(T^(2))= (g)/(4pi^(2))= "constant"` <br/> at a given place ……………(2) <br/> If `T_(1)` and `T_(2)` are the time periods of the pendulum for length `l_(1)` and `l_(2)`. From Eq(2) we cab <a href="https://interviewquestions.tuteehub.com/tag/write-746491" style="font-weight:bold;" target="_blank" title="Click to know more about WRITE">WRITE</a> <br/> `(l_(1))/(T_(1)^(2))= (l_(2))/(T_(2)^(2))`..............(2) <br/> Here `T_(1)=2s` when `l_(1)= 1.02m` when `l_(2)= 0.5 m, T_(2)=? `<br/> Using Eq. (3)`(1.02)/(2^(2))= (0.51)/(T_(2)^(2))` or `T_(2)^(2)= (0.51)/(1.02) xx 4 =2 ` <br/> `:. T_(2)= sqrt(2) = 1.414 s` When the lenght increases the time period of the pendulum increases. So the clock loses time or <a href="https://interviewquestions.tuteehub.com/tag/runs-1192287" style="font-weight:bold;" target="_blank" title="Click to know more about RUNS">RUNS</a> slow.</body></html>