The iron door of a building is 3 m broad which can be opened by applying a force of 100 N normally at the middle of the door. The least force and its point of application to open the door should be ___________.

150 N at the middle of the door

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150 N at the free end of the door

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50 N at the middle of the door

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50 N at the free end of the door

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Solution

The correct option is D 50 N at the free end of the door
Torque depends on the amount of force applied as well as the perpendicular distance between the axis of roation and the line of action of force. Least force is required when the distance involved is more. Here, the torque on the application of force at the middle will be equal to the torque on the application of force at the free end of the door. Thus,
$100 N \times 1.5 m$ = Least force $\times 3 m$
Least force = $150 N m / 3 m = 50 N$ (At the free end of the door)

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The iron door of a building is 3 m broad which can be opened by applying a force of 100 N normally at the middle of the door. The least force and its point of application to open the door should be ___________.​

The iron door of a building is 3 m broad which can be opened by applying a force of 100 N normally at the middle of the door. The least force and its point of application to open the door should be ___________.