A lift is moving vertically upwards with an acceleration a. What will be the changed time period of a simple pendulum suspended from the roof of the lift? If the lift becomes free and starts falling down with the acceleration due to gravity, what will be the change in the time period?

A lift is moving vertically upwards with an acceleration a. What will

1.	A lift is moving vertically upwards with an acceleration a. What will be the changed time period of a simple pendulum suspended from the roof of the lift? If the lift becomes free and starts falling down with the acceleration due to gravity, what will be the change in the time period?
Answer» SOLUTION :ACCELERATION due to gravity (downwards) = g Acceleration of the LIFT (upwards) = -a Hence, the effective acceleration due to gravity with respect to the lift, `g.=g-(-a)=g+a` Therefore, the time period of the pendulum in the lift, `T.=2pisqrt(L/(g+a))` We compare it with the time period inside the lift with no acceleration: `T=2pisqrt(L/g)` `therefore" "T/(T.)=sqrt((g+a)/g)or,T.=Tsqrt(g/(g+a))` As `glt(g+a),T.ltT`, hence, in this CASE, the time period will decrease. When the lift is falling freely downwards, its acceleration a = g. Hence, the acceleration due to gravity with respect to the lift, g. = g - a = g - g = 0 Hence, the time period, in this case, `T.=2pisqrt(L/(g.))` = infinity. Infinite time period signifies that the pendulum will not oscillate at all.