To solve the problem of finding the force that must be applied at one end of a lever to keep it in horizontal equilibrium, we can use the principles of moments (torque). Let's break down the problem step-by-step. ### Step 1: Understand the Setup - We have a uniform lever that is 90 cm long. - A load of 30 N is suspended 15 cm from one end of the lever. - The fulcrum (pivot point) is located at the center of the lever, which is at 45 cm from either end. ### Step 2: Identify Distances - The distance from the fulcrum to the load (30 N) is: \[ \text{Distance from fulcrum to load} = 45 \text{ cm} - 15 \text{ cm} = 30 \text{ cm} \] - The distance from the fulcrum to the point where we will apply the force (let's call this force \( F \)) is: \[ \text{Distance from fulcrum to applied force} = 90 \text{ cm} - 45 \text{ cm} = 45 \text{ cm} \] ### Step 3: Apply the Principle of Moments For the lever to be in horizontal equilibrium, the clockwise moments must equal the counterclockwise moments about the fulcrum. - **Clockwise Moment due to the Load**: \[ \text{Moment} = \text{Force} \times \text{Distance} = 30 \text{ N} \times 30 \text{ cm} = 900 \text{ N cm} \] - **Counterclockwise Moment due to the Applied Force**: \[ \text{Moment} = F \times 45 \text{ cm} \] ### Step 4: Set Up the Equation To maintain equilibrium: \[ \text{Clockwise Moment} = \text{Counterclockwise Moment} \] This gives us the equation: \[ 30 \text{ N} \times 30 \text{ cm} = F \times 45 \text{ cm} \] Substituting the moments: \[ 900 \text{ N cm} = F \times 45 \text{ cm} \] ### Step 5: Solve for \( F \) To find \( F \), we rearrange the equation: \[ F = \frac{900 \text{ N cm}}{45 \text{ cm}} = 20 \text{ N} \] ### Conclusion The force that must be applied at the other end of the lever to keep it in horizontal equilibrium is **20 N**. Therefore, the correct option is **B**. ### Explanation of Other Options - **Option A (15 N)**: This is incorrect because it does not provide enough counterclockwise moment to balance the 900 N cm of clockwise moment created by the load. - **Option C (30 N)**: This would create a counterclockwise moment of \( 30 \text{ N} \times 45 \text{ cm} = 1350 \text{ N cm} \), which is too large compared to the 900 N cm from the load. - **Option D (60 N)**: This would create an even larger counterclockwise moment of \( 60 \text{ N} \times 45 \text{ cm} = 2700 \text{ N cm} \), which is also excessive. ### Revision Summary - The lever is in equilibrium when clockwise moments equal counterclockwise moments. - Calculate moments using the formula: Moment = Force × Distance from the fulcrum. - Ensure to correctly identify distances from the fulcrum for both the load and the applied force. - The correct force to maintain equilibrium in this scenario is 20 N.