Are uniform metre rule of mass 120 grams is 60cm Mark at what point on the metre rule should a mass of 50 grams be suspended for it to balance horizontally
To determine the point on the meter rule where a mass of 50 grams should be suspended for the meter rule to balance horizontally, you need to understand the concept of moments and the principle of moments.
The principle of moments states that the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point when an object is in equilibrium.
In this case, you have a uniform meter rule with a mass of 120 grams and a length of 60 cm. This means that the center of mass is located at the midpoint of the meter rule, which is 30 cm.
To balance the meter rule, the sum of the clockwise moments should be equal to the sum of the anticlockwise moments. The moment of a force is calculated by multiplying the force by its perpendicular distance from the pivot point.
Let's assume the point where the 50-gram mass should be suspended is marked as "x" cm from the left end of the meter rule. The distance from the left end of the meter rule to the center of mass is 30 cm, and the distance from the left end to the point where the 50-gram mass is suspended is x cm.
The clockwise moment is calculated by multiplying the mass by its distance from the pivot point, and the anticlockwise moment is calculated by multiplying the mass by its distance from the pivot point.
Clockwise moment = 50 grams * (30 cm + x cm)
Anticlockwise moment = 120 grams * (30 cm)
For the meter rule to balance, the clockwise moment should be equal to the anticlockwise moment.
50 grams * (30 cm + x cm) = 120 grams * (30 cm)
Now, we can solve this equation to find the value of x.
50 grams * (30 cm + x cm) = 120 grams * (30 cm)
1500 grams * cm + 50 grams * x cm = 3600 grams * cm
50 grams * x cm = 3600 grams * cm - 1500 grams * cm
50 grams * x cm = 2100 grams * cm
x cm = 2100 grams * cm / 50 grams
x cm = 42 cm
So, a mass of 50 grams should be suspended at the 42 cm mark from the left end of the meter rule for it to balance horizontally.