Question

A simple pendulum is suspended from the ceiling of an empty box falling in air near earth surface. The total
mass of system is M. The box experiences air resistance R=-kv where v is the velocity of box and k is a
positive constant. After some time it is found that period of oscillation of pendulum becomes double the
value when it would have suspended from a point on earth. The velocity of box at that moment (take g in air
same as on earth's surface)
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Answer 1

Thus the value acceleration is a = 3g

Explanation:

A simple pendulum is suspended from the ceiling of a lift. When the lift is at rest its time period is T. With what acceleration should the lift be accelerated upwards in order to reduce its period to T/2? (g is acceleration due to gravity).

Solution:

T = 1/2π  √  l / g

Tf =  1/2π   √ l /g(eff)

g (eff) = g + a

Tf = T / 2

a = 3g

Thus the value acceleration is a = 3g