Question

EACH MULTIPLE CHOICE QUESTION IS WORTH 4 POINTS 1) Four forces of the same magnitude act on a rectangle that can rotate about point P at the midpoint of the bottom edge. Rank the magnitudes of the torques (from largest to smallest) caused by these four forces about point P. Point P is the hinge or axis of rotation. F A) T2 > > > B) T4 > 73 > C) T3 > 1 D) T > T2 > TA > 73 E) TA > T2 > > T3 v v vvv
explain your reasoning

Answer 1

We know torque $\vec{T}=\vec{r}\times \vec{F}$

  $or\: \: \: \: \: \vec{T}=\left | \vec{r} \right |.\left | \vec{F} \right |\sin \Theta$

For this problem $\Theta$ =90o.

  $\therefore \: \: \: \: \: \vec{T}=\left | \vec{r} \right |.\left | \vec{F} \right |\: \: \: \: \: \: \: \: (i)$

Here r is the perpendicular distance and F is the magnitude of the applied force.

Let the perpendicular distance for F1=r1 .

Let the perpendicular distance for F2=r2.

     Let the perpendicular distance for F3=r3.

   Let the perpendicular distance for F4=r4.

From the figure we can say

$r_{4}> r_{2}> r_{1}> r_{3}\: \: \: \: \: \: \left [ \: \: \: r_{3}=0\: \: \right ]$

From the equation (i) we can say option  

     $(E)\: \: \: \: \: \: \: T_{4}> T_{2}> T_{1}> T_{3}\: \: \: \: \: \: \left [ \: \: \: T_{3}=0\times F_{3}=0\: \: \right ]$

is correct.