Try this problem useful for the Physics Olympiad based on Motion of an Elevator.

**The Problem: Motion of an Elevator**

An elevator of mass *M *is accelerated upwards by applying a force *F*. A mass *m *initially situated at a height

of 1m above the floor of the elevator is falling freely. It will hit the floor of the elevator after a time equal to

- √(2M/F+mg)
- √(2M/F-mg)
- √2M/F
- √2M/(F+Mg)

**Discussion:**

Acceleration of elevator a_{e}= F/M ( in upward direction)

Acceleration due to gravity is in downward direction so acceleration of mass a_{s}= -g

Acceleration of mass with respect to elevator

= a_{s}-a_{e}

=(F/M)+g

=(F+Mg)/M

We know,

s=ut+(1/2)at^{2}

From the given problem, we have s=1m

so,

1=(F+Mg)t^{2}/M

t=√2M/(F+Mg)

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