Final Answer:
YS is the state 30. A lover of negligible weight is on one side of a beam with a 30N weight at one end and a 40N weight at the other. Then, the fulcrum is 6 units away from the 30N weight. Thus, the correct answer is B) 6 meters.
Explanation:
The problem presents a situation where a lover of negligible weight (considered a point load) is on one side of a beam, with a 30N weight at one end and a 40N weight at the other. To determine the distance of the fulcrum from the 30N weight, we can apply the principle of moments, also known as torque, considering the clockwise and anticlockwise moments to be equal in equilibrium.
The principle of moments states that the sum of the anticlockwise moments about a point equals the sum of the clockwise moments about the same point. Mathematically, the equation is:
Force × Distance from fulcrum = Force × Distance from fulcrum
For the given scenario:
30N × Distance of the 30N weight from the fulcrum = 40N × Distance of the 40N weight from the fulcrum
30 × d1 = 40 × d2
To find the distance of the fulcrum from the 30N weight:
d1 = (40 × d2) / 30
d1 = (40 × d2) / 30
d1 = (4/3) × d2
Given the options, the closest distance that satisfies this equation is when d1 = 4 and d2 = 3. Therefore, the distance of the fulcrum from the 30N weight is 4 units, and consequently, from the 40N weight is 3 units. Hence, the fulcrum is 6 units away from the 30N weight, making the correct answer B) 6 meters.
Thus, the correct answer is B) 6 meters.