A metre scale has a weight of 10 grams at a distance of 20 cm from the pivot. To balance this a student places another weight at a distance of 35 cm. Calculate the mass of this weight.
Question
A metre scale has a weight of 10 grams at a distance of 20 cm from the pivot. To balance this a student places another weight at a distance of 35 cm. Calculate the mass of this weight.
Solution
To solve this problem, we need to use the principle of moments. The principle of moments states that for a body to be in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point.
Step 1: Identify the forces and their distances from the pivot.
- The weight of the meter scale is 10 grams (which is 0.01 kg if we convert it to kilograms) and it is 20 cm (or 0.2 m in meters) from the pivot.
- The unknown weight (let's call it W) is 35 cm (or 0.35 m in meters) from the pivot.
Step 2: Set up the equation using the principle of moments.
- The meter scale is creating a clockwise moment and the unknown weight is creating an anticlockwise moment. So, we can set up the equation as follows: (0.01 kg * 9.8 m/s^2 * 0.2 m) = (W kg * 9.8 m/s^2 * 0.35 m)
Step 3: Solve the equation for W.
- First, simplify both sides of the equation: (0.01 kg * 9.8 m/s^2 * 0.2 m) = 0.0196 Nm and (W kg * 9.8 m/s^2 * 0.35 m) = 3.43W Nm
- Then, set these two expressions equal to each other and solve for W: 0.0196 Nm = 3.43W Nm, so W = 0.0196 Nm / 3.43 Nm = 0.0057 kg
So, the mass of the weight that the student needs to place at a distance of 35 cm to balance the meter scale is approximately 0.0057 kg, or 5.7 grams when converted back to grams.
Similar Questions
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