A metre rule is found to balance horizontally at the 48cm marked when the body mass of 60G is suspended at the 6cm marked..A balance point is marked to be 30cm.calculate
(1)The mass of the metre rule ( 2)The distance of the balanced point from the zero end if the body were moved to 30cm mark
To find the answers to the given questions, we can apply the principle of moments. The principle of moments states that for a body to be in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.
Let's solve each question step by step:
(1) To find the mass of the meter rule:
Let's assume the mass of the meter rule is M grams.
The 60g mass is suspended at the 6cm mark. So, the clockwise moment is 60g multiplied by the distance from the zero end (anticlockwise to clockwise direction), which is 6cm.
The meter rule balances horizontally at the 48cm mark, so the anticlockwise moment is (M grams) multiplied by the distance from the zero end (clockwise to anticlockwise direction), which is 48cm.
Setting up the equation as per the principle of moments:
Clockwise moment = Anticlockwise moment
60g * 6cm = M grams * 48cm
Converting grams to kilograms and centimeters to meters for consistency:
0.06kg * 0.06m = (M/1000)kg * 0.48m
Simplifying the equation:
0.0036kg = (M/1000) * 0.48
Now, we can solve for the mass of the meter rule (M):
0.0036kg = (0.48/1000) * M
0.0036kg = 0.00048kg * M
Dividing both sides of the equation by 0.00048kg:
M = 0.0036kg / 0.00048kg
M = 7.5kg
Therefore, the mass of the meter rule is 7.5 kilograms.
(2) To find the distance of the balance point from the zero end when the body is moved to the 30cm mark:
Let's assume the distance from the balance point to the zero end when the body is moved to the 30cm mark is D cm.
The 60g mass is now suspended at the 30cm mark. So, the clockwise moment is 60g multiplied by the distance from the zero end (anticlockwise to clockwise direction), which is D cm.
The meter rule balances at the 48cm mark, so the anticlockwise moment is (M grams = 7.5kg) multiplied by the distance from the zero end (clockwise to anticlockwise direction), which is (48 - 30) cm.
Setting up the equation as per the principle of moments:
Clockwise moment = Anticlockwise moment
60g * D cm = 7.5kg * (48 - 30) cm
Converting grams to kilograms and centimeters to meters for consistency:
0.06kg * (D/100) m = 7.5kg * (18/100) m
Simplifying the equation:
0.006kg * D = 1.35kg
Now, we can solve for the distance (D):
D = 1.35kg / 0.006kg
D = 225 cm
Therefore, the distance of the balanced point from the zero end when the body is moved to the 30cm mark is 225 cm.