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A door is hinged at one end and is free o rotate about a vertical axis (Fig.) does it weight cause any torque about this axis? Give reason for your answer.

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Let us consider the given diagram, where weight of the door acts along negative y-axis.

A force can produce torque only along a direction normal to itself as τ = r × f. So, when the door is in the xy-plane, the torque produced by gravity can only be ±z direction, never about an axis passing thoroughly y direction.

Hence, the weight will not produce any torque about y-axis.

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