A simple seconds pendulum is constructed out of a very thin string of thermal coefficient of linear expansion `alpha = 20 xx 10^(-4)//^(@)C` and a heavy particle attached to one end. The free end of the string is suspended from the ceiling of an elevator at rest. the pendulum keeps correct time at `0^(@)C`. when the temperature rises to `50^(@)C`, the elevator operator of mass `60 kg` being a student of Physics accelerates the elevator vertically, to have the pendulum correct time. the apparent weight of the operator when the pendulum keeps correct time at `50^(@)C` is `("Take " g = 10m//s^(2)`)

Options

A. `660 N`
B. `440 N`
C. `520 N`
D. `340 N`

Answer

A

Explanation

`T = 2 pi sqrt((l)/(g))`
When the temperature is raised length changes to
`l(1+alpha Delta T)`
When the lift acceleration upwards
`g_("eff") = g+a`
new period of pendulum
`T' = 2 pi sqrt((l(1+alpha DeltaT))/(g+a))`
`T'=TrArr "g" ((1+alpha Delta T))/((g+a)) = 1`
or `a=g alpha DeltaT = 10xx20xx10^(-4)xx5.0 = 1m//sec^(2)`
`W_(eff) = m(g+a)`
`=60(10+1)=660N`.