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Two pendulums of length 90 cm and 100 cm start oscillating in phase. After how many osxillations will they b again in the same phase ? |
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Answer» The two pendulums will be in same phase again when pendulum of large length completes v oscillations in time t and small pendulum completes `(v+1)` oscillations in time t. For pendulum of large length, `(v)/(t)=(1)/(2pi)sqrt((g)/(l))=(1)/(2pi)sqrt((g)/(100))` and `(v+1)/(t)=2pisqrt((g)/(90))` `:. (v+1)/(v)=sqrt((100)/(90))=(sqrt(10))/(3)=(3.162)/(3)=1.054` `1+(1)/(v)=1.054 or (1)/(v)=1.054-1=0.054` or `v=(1)/(0.054)=18.5` Thus the two pendulums will be in same phase when the pendulum of larger length completes 18.5 oscillations and pendulum of smaller length completes `18.5+1=19.5` oscillations. |
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