Alift is ascending with acceleration g/3. what will be the time period of a simple pendulum suspended from the ceiling if its time period in stationary lift is t

Here is how you get the answer to this question.
Given that the ascending is with an acceleration of g/3, now, let's look for the time period of a simple pendulum suspended from the ceiling, given that its time period in stationary lift is T.
So, 
Fnet = T - mg
Fnet = ma = T - mg
m(g/3) = T-mg
T=4mg/3
This tension decides the apparent weight, and therefore the apparent "g"
so apparent g= 4g/3 now,T=2π √ l/g(apparent) therefore,T′=3–√/2T
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