The iron door of a building is $x$ m broad. It can be opened by applying a force of $F_{1} N$ at the middle of the door. Calculate the least force which can open the door in terms of $F_{1}$ .

F_{1} / 2

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F_{1}

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F_{1} / 4

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F_{1} / x

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Solution

The correct option is A $F_{1} / 2$
We know that door can be opened only if a torque is applied on it.
Let $ $τ$ be torque required to open the door then,
$τ = \frac{F_{1} x}{2}$
To open the door by applying minimum force, we have to apply the force $(F_{2})$ at the end of the door
$\Rightarrow F_{2} x = τ = \frac{F_{1} x}{2}$

$\Rightarrow F_{2} = \frac{F_{1}}{2}$
Therefore, A is correct option.

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The iron door of a building is x m broad. It can be opened by applying a force of F1N at the middle of the door. Calculate the least force which can open the door in terms of F1.

The iron door of a building is $x$ m broad. It can be opened by applying a force of $F_{1} N$ at the middle of the door. Calculate the least force which can open the door in terms of $F_{1}$ .