A metre rule is found to balance at the 54cm mark when a body of mass 80g is suspended at the 20cm mark ,the balance point is said to be at 55cm mark. Calculate the mass of the ruler and the distance of the balance point from the zero end,if the body were moved to the 15cm mark.
I do not understand. If the cg of stick is at 54 it does not move up to 55 when you add mass at 20.
Please check for typos.
The question is calculate the meter ruler of weight 2N is found to balance at 50cm mark. Find its new turning point when a body of mass 250g is suspended at the 5cm mark
To solve this problem, we need to apply the principle of moments. The principle of moments states that the sum of the clockwise moments about a point is equal to the sum of the anticlockwise moments about the same point.
Let's assign some variables:
- Mass of the ruler: M (to be determined)
- Distance of the balance point from the zero end: x (to be determined)
- Mass of the body: 80g
- Distance of the body from the zero end (initially): 20cm
- Distance of the body from the zero end (after moving): 15cm
- Distance of the balance point from the zero end (initially): 54cm
- Distance of the balance point from the zero end (after moving): 55cm
Using the principle of moments, we can set up the equation:
(clockwise moments) = (anticlockwise moments)
(Mass of the body) × (Distance of the body from the zero end) = (Mass of the ruler) × (Distance of the balance point from the zero end)
(80g) × (20cm) = (M) × (54cm)
Now, let's rearrange the equation to solve for the mass of the ruler, M:
M = (80g × 20cm) / (54cm)
M = (1600g·cm) / (54cm)
M ≈ 29.63g
The mass of the ruler is approximately 29.63g.
Next, let's find the distance of the balance point from the zero end (x) when the body is moved to the 15cm mark:
(Mass of the body) × (Distance of the body from the zero end after moving) = (Mass of the ruler) × (Distance of the balance point from the zero end after moving)
(80g) × (15cm) = (29.63g) × (x)
Solving for x:
x = (80g × 15cm) / (29.63g)
x = 40.32cm
The distance of the balance point from the zero end, when the body is moved to the 15cm mark, is approximately 40.32cm.