When a mass of 50g is hung from 5cm mark of a uniform meter rule. The rule balance on a knife edge placed at the 35cm mark . what is the weight of d meter rule? (take g:10ms-2).
moments in grams * centimeters about 0 cm mark
clockwise: 50 * 5 + m * 50
counterclockwise: (m+50) * 35
so
250 + 50 m = 35 m + 1750
15 m = 1500
m = 100 grams which is 0.100 kilograms
weight = mass * g = 0.100 kg * 10 meters /second^2 = 1 Newton
oops ... forgot to double the 50 g
weight of the rule is ... 1 N
To find the weight of the meter rule, we need to calculate the sum of the weights acting on each side of the knife edge.
Let's break down the problem step by step:
Step 1: Determine the weight of the 50g mass.
The weight (W) of an object can be calculated using the formula:
W = mass (m) x acceleration due to gravity (g).
As given, the mass of the object is 50g. However, we need to convert it to kilograms, since the standard unit for mass is kg.
1 kg = 1000 g
Therefore, the mass (m) is 50g รท 1000g/kg = 0.05 kg.
Now, we can calculate the weight (W) using the formula:
W = 0.05 kg x 10 m/s^2 = 0.5 N.
Step 2: Determine the distance of the 50g mass from the knife edge.
The 50g mass is hung from the 5cm mark of the meter rule. Since the meter rule is 100 cm long, we can calculate the distance of the 50g mass from the knife edge:
Distance = Total length - Distance from knife edge.
Total length = 100 cm.
Distance from knife edge = 5 cm.
Distance = 100 cm - 5 cm = 95 cm.
Step 3: Calculate the weight acting on each side of the knife edge.
Since the meter rule is balanced, the sum of the weights on each side should be zero.
Let's assume the weight of the meter rule is W'.
Weight on the left side of the knife edge = W (weight of the 50g mass) + W' (weight of the meter rule).
Weight on the right side of the knife edge = W' (weight of the meter rule).
Since the meter rule is balanced, the total weight on the left side of the knife edge should be equal to the total weight on the right side.
Therefore, we can set up the equation:
(Weight on the left side) - (Weight on the right side) = 0.
Weight on the left side = W + W'.
Weight on the right side = W'.
(W + W') - W' = 0.
Simplifying the equation, we get:
W = W'.
So, the weight of the meter rule is equal to the weight of the 50g mass, which is 0.5 N.
the 50 g mass is 30 cm from the balance point
the center of mass of the meter rule is 15 cm from the balance point
... half the distance ... twice the mass
the mass of the rule is twice 50 g
... weight is ... m * g ... .05 kg * 10 m/s^2 = .5 N