Two pendulums of lengths in the ratio 9:1 start oscillating at t=0.they will again be in phase after the shorter pendulum has made n oscillations the value of n is

A]2           b]3           c]1\2    d]3\2

Asked by shubham.padamwar.3 | 25th Apr, 2015, 09:12: PM

Expert Answer:

Time period of a pendulum is given by:
 
begin mathsize 12px style straight T equals 2 straight pi square root of straight l over straight g end root straight i. straight e. space straight T space straight alpha space square root of straight l This space indicates space that space time space period space of space shorter space pendulum space will space be space smaller comma space straight i. straight e. space it space will space complete space more space oscillations space in space the space same space time space than space the space longer space pendulum. space If space straight T subscript straight S space and space straight T subscript straight L space are space the space time space periods space of space shorter and space longer space pendulum comma space then space the space two space pendulum space will space be space in space same space phase space for space the space first space time space when space the space shorter space has space completed space straight n space oscillations space and space longer space one space left parenthesis straight n minus 1 right parenthesis space oscillations. Hence space we space can space write space that colon nT subscript straight S space equals space open parentheses straight n minus 1 close parentheses straight T subscript straight L straight T subscript straight S over straight T subscript straight L equals fraction numerator open parentheses straight n minus 1 close parentheses over denominator straight n end fraction straight T subscript straight S over straight T subscript straight L equals fraction numerator square root of straight l subscript straight S end root over denominator square root of straight l subscript straight L end root end fraction equals fraction numerator open parentheses straight n minus 1 close parentheses over denominator straight n end fraction Given space straight l subscript straight S space end subscript colon straight l subscript straight L equals space 1 colon 9 fraction numerator open parentheses straight n minus 1 close parentheses over denominator straight n end fraction equals 1 third 3 left parenthesis straight n minus 1 right parenthesis equals straight n 3 straight n minus 3 equals straight n 2 straight n equals 3 straight n equals 3 over 2 end style

Answered by Jyothi Nair | 27th Apr, 2015, 12:16: PM