### Determining the Correct Torque EquationIn this section, we aim to understand how to balance torques to determine the correct torque equation. The following diagram and question illustrate a common physics problem involving a hinged bar attached to a wall with a rope and a hanging weight.#### Diagram DescriptionThe diagram shows a bar hinged to a wall at one end, with a rope attached to the other end of the bar, making a 45-degree angle with the bar. The bar itself is inclined at a 20-degree angle from the horizontal when it is pivoted at the hinged point. A weight of 400 N is hanging from the free end of the bar.#### Variables:- \( L \): The length of the bar- \( M \): The mass of the bar- \( T \): The tension in the rope- \( F \): The force at the hinge- \( g \): Acceleration due to gravity#### Question:Based on the diagram, place the pivot point at the hinge on the wall and determine which of the following torque equations is correctly written.Here are the listed options:1. \( T L \sin(65^\circ) = 400L \sin(70^\circ) + M g \left(\frac{L}{2}\right) \sin(70^\circ) \)2. \( T L \sin(65^\circ) = 400 \sin(70^\circ) - M g \left(\frac{L}{2}\right) \sin(70^\circ) \)3. \( T L \sin(45^\circ) = 400L \cos(20^\circ) + M g \left(\frac{L}{2}\right) \cos(20^\circ) \)### Explanation of TorqueTorque (\( \tau \)) is a measure of the rotational force acting on an object around a pivot point and is calculated by the equation:\[ \tau = r \times F \times \sin(\theta) \]where:- \( r \) is the distance from the pivot point to the point where the force is applied,- \( F \) is the force,- \( \theta \) is the angle between the force and the lever arm.For the equilibrium of torques, the sum of the clockwise torques must equal the sum of the counterclockwise torques.#### Analysis1. **First Equation**:

Answered: Image /qna-images/answer/fdbaed1b-9465-4f05-8295-3285ccd33fa2.jpg

Looking at the image below, and placing the pivot point at the hinge on the wall, determine which of the following torque equation is correctly written. Call L the length of the bar, M the mass of the bar, T the tension on the rope, F the force at the hinge. 45% 20° 400 N O TL sin(65) = 400L sin(70) + Mg() sin(70) O TL sin(65) = 400 sin(70) + MgL sin(70) O TL sin(45) = 400L cos (20) + Mg() cos(20)

Looking at the image below, and placing the pivot point at the hinge on the wall, determine which of the following torque equation is correctly written. Call L the length of the bar, M the mass of the bar, T the tension on the rope, F the force at the hinge. 45% 20° 400 N O TL sin(65) = 400L sin(70) + Mg() sin(70) O TL sin(65) = 400 sin(70) + MgL sin(70) O TL sin(45) = 400L cos (20) + Mg() cos(20)