**AP Physics 1 Question 326: Answer and Explanation**

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**Question: 326**

**4.** As it is, the system above is not balanced. Which of the following changes would NOT balance the system so that there is 0 net torque? Assume the plank has no mass of its own.

- A. Adding a mass equal to
*m*_{2}on the far left side and a mass equal to*m*_{1}and on the far right side - B. Stacking both masses directly on top of the fulcrum
- C. Moving the fulcrum a distance
*L*/3 to the right - D. Moving both masses a distance
*L*/3 to the left

**Correct Answer:** A

**Explanation:**

**A**

In this situation, the left-hand block will provide counterclockwise torque, and the right-hand block will provide clockwise torque. Therefore, the two must be equal in magnitude for the system to be balanced. You know that the formula for torque is *τ* = *Fr*sin*θ*. In this problem, *θ* will always be 90 degrees, and sin 90° = 1, so that term will be neglected for the rest of the explanation. Furthermore, the only forces involved in this problem are the forces of gravity on the blocks, and you know *F*_{g} = *mg.*

For (A), the net counterclockwise torque (left side of the system) would be *τ* = (*m*_{2}*g*)(2*L*) + (*m*_{1}*g*)(*L*) = (2*m*_{1}*g*)(2*L*) + (*m*_{1}*g*)(*L*) = 5*m*_{1}*gL.* The clockwise torque (right side of the system) would be *τ* = (*m*_{2}*g*)(*L*) + (*m*_{1}*g*)(2*L*) = (2*m*_{1}*g*)(*L*) + (*m*_{1}*g*)(2*L*) = 4*m*_{1}*gL*. Thus, it would not be balanced. Choice (B) would make both torques 0, so that would be balanced. Choices (C) and (D) both result in the fulcrum being twice as far from *m*_{1} as it is from *m*_{2}, which would counteract the difference in their weights.