a uniform half metre rule is freely pivoted at the 20 cm mark and its balance horizontaly when a body of mass 30g is hung 5cm mark from end calculate the mass of rule
the 30g mass is 20-5 = 15 cm left of pivot
the ruler mass m is 50-20 = 30 cm right of pivot
so
30 g * 15 cm = m * 30
m = 15 grams
m=15g
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15 grams
Well, I could calculate the mass of the ruler for you, but I might need an extra hand... or should I say, an extra half-meter? 🤡
Let's see. We know that the ruler is balanced horizontally when a 30g body is hung 5cm from one end. The ruler's center of mass must be at the 20cm mark in order for it to balance.
So, the center of mass is located 15cm away from where the 30g body is hanging (20cm - 5cm). If the ruler is in equilibrium, we know that the torque (or turning effect) on one side of the pivot must be equal to the torque on the other side.
The torque is calculated by multiplying the force (weight) acting on an object by the perpendicular distance from the pivot. In this case, the force is the mass of the body (30g) times the gravitational acceleration (9.8 m/s^2), and the perpendicular distance is 15cm.
So, torque on one side = torque on the other side:
(30g) * (9.8 m/s^2) * (15cm) = (mass of ruler) * (9.8 m/s^2) * (20cm)
Now, let's convert the units to make it less confusing:
(0.03kg) * (9.8 m/s^2) * (0.15m) = (mass of ruler) * (9.8 m/s^2) * (0.20m)
We can cancel out the common factors:
0.03 * 0.15 = (mass of ruler) * 0.20
0.0045 = (mass of ruler) * 0.20
Now, solving for the mass of the ruler:
Mass of ruler = 0.0045 / 0.20 = 0.0225 kg
So, the mass of the rule is approximately 0.0225 kg.
To calculate the mass of the rule, we can use the principle of moments. The principle of moments states that the sum of the moments on one side of a pivot point is equal to the sum of the moments on the other side of the pivot point.
In this given situation, the rule is balanced horizontally, which means that the sum of the moments is equal to zero.
Let's break down the moments involved in this situation:
1. Moment of the rule: The moment of the rule is the product of its mass and its distance from the pivot point. Let's assume the mass of the rule is "m" grams, and its length is half a meter or 50 cm. The distance of the rule's center of mass from the pivot point is 20 cm (as stated in the question). Therefore, the moment of the rule is m * 20 cm.
2. Moment of the hanging body: The moment of the hanging body is the product of its mass and its distance from the pivot point. Given that the mass of the hanging body is 30 grams and it is placed at the 5 cm mark from the end of the rule, the moment of the hanging body is 30 * 5 cm.
Since the rule is balanced horizontally, the sum of the moments on both sides of the pivot point is equal to zero:
Moment of the rule = Moment of the hanging body
m * 20 cm = 30 * 5 cm
To solve for the mass of the rule (m), we can rearrange the equation:
m = (30 * 5 cm) / 20 cm
m = 7.5 grams
Therefore, the mass of the rule is 7.5 grams.