a body mass 50g is suspended at the 20cm mark of a uniform meter rule. the meter rule is adjusted on a pivot until it balances horizontally at the 40cm mark. find the mass of the rule?
massrule*(50-40)=50*(40-20)
physics
To solve this problem, we can use the principle of moments. The total anticlockwise moment caused by the suspended body should be equal to the total clockwise moment caused by the rule. The formula for calculating the moment is:
Moment = Force × Distance
Let's assume the mass of the rule is M grams.
The moment caused by the suspended body is:
Moment_suspended body = (mass of the body) × (distance of the body from the pivot)
Moment_suspended body = 50g × 20cm = 1000 g.cm
The moment caused by the rule itself is:
Moment_rule = (mass of the rule) × (distance of the rule from the pivot)
Moment_rule = M g × 40cm = 40M g.cm
Since the rule is balanced, the two moments should be equal:
1000 g.cm = 40M g.cm
Dividing both sides of the equation by 40, we get:
25 g = M
Therefore, the mass of the rule is 25 grams.
To find the mass of the meter rule, we need to use the principle of moments. The principle of moments states that the sum of the clockwise moments is equal to the sum of the anticlockwise moments.
In this case, the moment of the mass of the rule is balanced by the moment of the suspended body.
Let's denote the mass of the rule as M, the distance from the pivot to the 50g body as x, and the distance from the pivot to the 40cm mark as y.
The moment of the 50g body can be calculated as follows:
Moment of the 50g body = Force x Distance
= 50g x x
And the moment of the meter rule can be calculated as:
Moment of the meter rule = Mass x Gravity x Distance
= M x g x y
Since the system is in equilibrium, the clockwise moment of the 50g body is balanced by the anticlockwise moment of the meter rule. So, we can write the equation:
50g x x = M x g x y
Now, let's substitute the values:
50g x 20cm = M x 9.8 m/s^2 x 40cm
We need to make sure that the units are consistent, so we convert cm to meters:
(50g x 0.20m) = (M x 9.8 m/s^2 x 0.40m)
Now we can solve for M:
M = (50g x 0.20m) / (9.8 m/s^2 x 0.40m)
M = 0.10 kg
Therefore, the mass of the meter rule is 0.10 kg.