A meter rule us found at 48cm mark when a body of mass 60g is supende 6cm mark the balance is found to be at 13cm mark class culate the (a) mass of the meter rule (b) distances of the balance point from zero end if the body were move to the 13cm mark
Seems like a straightforward physics balancing question. Where are you getting stuck on this?
the mass of the metre ruler (2) the distance of the balance point from zero end if the were moved to the 13cm mark
To calculate the mass of the meter rule, we will use the principle of moments.
(a) Mass of the meter rule:
The principle of moments states that the sum of the anticlockwise moments is equal to the sum of the clockwise moments.
Let's assume the balance point is at distance x from the zero end. The anticlockwise moment is the mass of the meter rule (M) multiplied by the distance from the balance point to the zero end (48 - x), and the clockwise moment is the mass of the body (60g) multiplied by the distance from the balance point to the 13cm mark (x - 13cm).
Setting up the equation:
M × (48 - x) = 60g × (x - 13cm)
Converting the mass of the body to kg:
60g = 0.06kg
Simplifying the equation:
48M - Mx = 0.06x - 0.78
Rearranging the equation to isolate M:
48M + 0.06x = Mx + 0.78
48M - Mx = 0.06x + 0.78
M(48 - x) = 0.06x + 0.78
M = (0.06x + 0.78) / (48 - x)
Now we can calculate the mass of the meter rule by substituting the given value of x (6cm) into the equation:
M = (0.06 × 6 + 0.78) / (48 - 6)
Calculating:
M = (0.36 + 0.78) / 42
M = 1.14 / 42
M ≈ 0.0271 kg
Therefore, the mass of the meter rule is approximately 0.0271 kg.
(b) Distance of the balance point from the zero end when the body is moved to the 13cm mark:
Let's assume the new balance point is at distance y from the zero end.
Using the principle of moments again, we have:
M × (48 - y) = 0.06kg × (y - 13cm)
Simplifying the equation:
48M - My = 0.06y - 0.78
We know the mass of the meter rule (M) is approximately 0.0271 kg from part (a). Now we can solve for y.
48 × 0.0271 - 0.0271y = 0.06y - 0.78
1.2996 - 0.0271y = 0.06y - 0.78
0.0871y = 2.0796
y ≈ 23.88 cm
Therefore, when the body is moved to the 13cm mark, the new balance point is approximately 23.88 cm from the zero end.
To solve this problem, we'll use the principle of moments (also known as torque). The principle of moments states that for an object to be balanced, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.
Before we start, let's define a few variables:
- MR represents the mass of the meter rule.
- MD represents the distance of the meter rule's center of mass from the zero end.
- BD represents the distance of the balance point from the zero end.
- BM represents the mass of the body.
Now let's solve the problem:
(a) Calculate the mass of the meter rule (MR):
To balance the system, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.
Clockwise moments = Force × Distance
Anticlockwise moments = Force × Distance
For the meter rule:
Clockwise moment = (MR × 9.8N/kg) × (48cm - MD)
Anticlockwise moment = (MR × 9.8N/kg) × MD
For the body:
Clockwise moment = (BM × 9.8N/kg) × (13cm - BD)
Anticlockwise moment = (BM × 9.8N/kg) × BD
Since the system is in equilibrium:
(MR × 9.8N/kg) × (48cm - MD) + (BM × 9.8N/kg) × (13cm - BD) = (MR × 9.8N/kg) × MD + (BM × 9.8N/kg) × BD
Now plug in the values:
(60g × 9.8N/kg) × (13cm - BD) = (MR × 9.8N/kg) × 6cm + (60g × 9.8N/kg) × BD
Solving this equation will give you the mass of the meter rule (MR).
(b) Calculate the distance of the balance point from the zero end if the body were moved to the 13cm mark:
For this scenario, we know the mass of the body and the distance of the body's center of mass from the zero end (13cm).
Using the same principle of moments, we can set up the equation again:
Clockwise moments = Force × Distance
Anticlockwise moments = Force × Distance
Clockwise moment = (MR × 9.8N/kg) × (48cm - MD)
Anticlockwise moment = (BM × 9.8N/kg) × (13cm - BD)
Since the system is in equilibrium:
(MR × 9.8N/kg) × (48cm - MD) + (BM × 9.8N/kg) × (13cm - BD) = (BM × 9.8N/kg) × BD
Now plug in the values:
(MR × 9.8N/kg) × (48cm - MD) = (60g × 9.8N/kg) × (13cm - BD)
You can solve this equation to find the distance of the balance point (BD) from the zero end.