Chapter 11, Problem 1CQ

Two forces produce the same torque. Does it follow that they have the same magnitude? Explain.

To determine

Whether the two forces have same magnitude or not when they produce same torque.

Answer to Problem 1CQ

No. The two forces do not have the same magnitude.

Explanation of Solution

Expression for the torque is,

$\tau =rF$

Here,

$r$ is the distance from the axis of rotation.

$F$ is the force applied.

From the above equation, the value of the torque is directly proportional to the force applied and the distance from the axis of the rotation.

Two forces can produce the same torque for both the cases, when the small force is applied farther from the axis of the rotation and when the large force is applied nearer from the axis of rotation.

The forces which have same in magnitude cannot produce the same torque because their distance from the axis of rotation is different.

Conclusion:

Therefore, it cannot be concluded that the two forces do not have the same magnitude.