Based on the principle of moments and the data provided;
- the mass of the rod is 20 kg
- the smallest value of X of the block that will keep the rod in equilibrium will be 4.054 kg
<h3>What is the principle of moments?</h3>
The principle of moments states that the for a body in equilibrium, the sum of the clockwise moments is equal to the sum of the anticlockwise moments about a point.
- Sum of Clockwise moments = Sum of Anticlockwise moments
- Moment of a force = mass × perpendicular distance.
At the point where the uniform rod is about to tilt, it is at equilibrium.
Anticlockwise moments = 30 × (1.3 - 0.5) = 24
Clockwise moments = m × (2.5 - 1.3)
where m is the mass of the end
Clockwise moments = m × 1.2
1.2 × m = 24
m = 20 Kg
Therefore, the mass of the rod is 20 kg
Assuming the boy moves to B and a block of mass X is placed at:
Anticlockwise moments = 30 × 1.3 = 39
Clockwise moments = 20 × 1.2 + X × 3.7
Clockwise moments = 24 + 3.7X
39 = 24 + 3.7X
3.7X = 15
X = 4.054 kg
Therefore, the smallest value of X of the block that will enable the boy to stand on the beam at B without the beam tilting is 4.054 kg
Assuming that the block is a particle allowed the assumption that the block touches the rod at only a point.
Learn more about principle of moments at: brainly.com/question/26117248
