A force was applied on a door in four ways. From the given top views for the door, the representation for zero torque is:

A force was applied on a door in four ways. From the given top views for the door, the representation for zero torque is: Correct Answer <img alt="F1 Jitendra Kumar Anil 05.04.21 D7" src="//storage.googleapis.com/tb-img/production/21/04/F1_Jitendra%20Kumar_Anil_05.04.21_D7.png" style="width: 138px; height: 137px;">

The correct answer is option 1) 

CONCEPT:

  • Torque: Torque is the turning effect produced on an object due to a force acting on it at a distance from a fixed point. The object tends to turn about this fixed point.
    • It is defined mathematically as the cross product of force and the perpendicular distance to an axis of rotation.
    • Consider a fore F acting at a distance r from a fixed point O as shown.

The torque produced is given by:

τ = r × F = rFsinθ 

  • The SI unit of torque is N-m.

[ alt="F1 Jitendra Kumar Anil 05.04.21 D1" src="//storage.googleapis.com/tb-img/production/21/04/F1_Jitendra%20Kumar_Anil_05.04.21_D1.png" style="width: 349px; height: 104px;">

  • Movement of doors: Doors have a fixed axis of rotation for their movement. The hinges provided on the edges of the doors help in the turning motion. When a force is applied on the doorknob, the perpendicular distance between the hinges and the doorknob acts as the moment arm. 

[ alt="F1 Jitendra Kumar Anil 05.04.21 D6" src="//storage.googleapis.com/tb-img/production/21/04/F1_Jitendra%20Kumar_Anil_05.04.21_D6.png" style="width: 343px; height: 210px;">

EXPLANATION:

Torque = Moment arm × Force applied = r × F = rFsinθ 

Hence, the torque produced will be zero if:

  1. either moment arm or force applied is zero
  2. the angle between moment arm and force is zero.
[ alt="F1 Jitendra Kumar Anil 05.04.21 D7" src="//storage.googleapis.com/tb-img/production/21/04/F1_Jitendra%20Kumar_Anil_05.04.21_D7.png" style="width: 138px; height: 137px;">
  • Here, the force is applied at the point of rotation. So, moment arm = 0.
  • Thus torque will be zero.
[ alt="F1 Jitendra Kumar Anil 05.04.21 D8" src="//storage.googleapis.com/tb-img/production/21/04/F1_Jitendra%20Kumar_Anil_05.04.21_D8.png" style="width: 141px; height: 197px;">
  • The force applied is perpendicular and far away from the point of rotation.
  • The maximum moment arm distance causes maximum torque.
  • Torque is not zero.
[ alt="F1 Jitendra Kumar Anil 05.04.21 D9" src="//storage.googleapis.com/tb-img/production/21/04/F1_Jitendra%20Kumar_Anil_05.04.21_D9.png" style="width: 137px; height: 197px;">
  • The force applied is perpendicular and away from the point of rotation.
  • So, torque will not be zero.
[ alt="F1 Jitendra Kumar Anil 05.04.21 D10" src="//storage.googleapis.com/tb-img/production/21/04/F1_Jitendra%20Kumar_Anil_05.04.21_D10.png" style="width: 137px; height: 135px;">
  • The force applied is perpendicular and away from the point of rotation.
  • So, torque will not be zero.

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