Question

why do we prefer to use a wrench with a long arm

Answer 1

it is due to more the perpendicular distance lesser the force applied because force is inversely proportional to distance. For example a steering wheel of large diameter is easy to rotate rather than the steering wheel which is having less diameter.
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Answer 2

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The perpendicular distance between the wrench and the axis of rotation is inversely proportional to force applied. In order to increase the torque, the length of the wrench is increased. In doing so, less force is used on the nut.

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