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Q. Two pendulums of lengths $1.44\, m$ and $1\, m$ start to swing together. The number of vibrations after which they will again start swinging together is

KEAMKEAM 2012Oscillations

Solution:

If t is the time taken by pendulums to come in same phase again first time after $t=0$.
Then, $(n-1) 2 \pi \sqrt{\frac{l_{1}}{g}} =n 2 \pi \sqrt{\frac{l_{2}}{g}} $
$(n-1) \times \sqrt{1.44} =n $
$(n-1) =1.2\,n $
$(n+1) =1.2\,n $
$n =\frac{1}{0.2}=5$