Chapter 8, Problem 3STP

To determine

To Choose: The correct option.

Answer to Problem 3STP

C. $0.2\text{m}$

Explanation of Solution

Given:

The torque required to remove the nut, $\tau =10\text{N-m}$

The maximum force child is capable of exerting at $90°$ , $F=50\text{N}$

Formula used:

The torque is given by,

  $\tau =Fr\sin \theta$

Where F is the applied force, r is the distance of the point of application of force from the axis of rotation, and $\theta$ is the angle between F and r .

Calculation:

The angle between the length of wrench and the force exerted by child will be, $\theta =90°$

Then, using the formula of torque, the length of wrench required is,

  $\begin{array}{c}\tau =Fr\sin \theta \\ 10=50r\sin 90°\\ r=0.2\text{m}\end{array}$

Conclusion:

Thus, the required length of wrench is $0.2\text{m}$ .