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 ?

Explanation

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.