Two forces are applied to a doorknob, perpendicular to the door. The first force is twice as large as the second force. The ratio of the torque of the first to the torque of the second is
A) 1/4.
B) 1/2.
C) 2.
D) 4.
E) 8.

Question

Quizplus · Accepted Answer

The torque (τ) of a force (F) applied at a distance (r) from the axis of rotation is given by τ = Fr. Since the forces are applied perpendicular to the door, the distance r is the same for both forces, and we can compare their torques simply by comparing the magnitudes of the forces. Let F1 be the larger force and F2 be the smaller force. Then we have F1 = 2F2, and the ratio of their torques is:

τ1/τ2 = (F1r)/(F2r) = (2F2r)/(F2r) = 2

So the answer is C, 2.

Two Forces Are Applied to a Doorknob, Perpendicular to the Door