A Uniform Metre rule is pivoted at a 60 cm mark. It is balanced by suspending a weight of 100 gf at 80cm mark. What is the weight of the metre rule?
Answers
Given:
A uniform meter rule is pivoted at a 60 cm mark.
It is balanced by suspending a weight of 100 gf at 80 cm mark.
To Find:
The weight of the meter scale.
Solution:
A uniform meter scale is pivoted at a 60 cm mark.
Since the scale is uniform , hence the weight is uniformly distributed.
Hence the weight of scale can be assumed to be acting at the center of mass of scale.
To balance the meter scale , moment about the pivot should be equal to 0.
weight suspended on scale to balance it = 100 gf at 80 cm mark.
that is 20 cm away from the pivot.
Hence the moment caused by weight suspended
M = F.r= 100(20) = 2000 gf cm.
Hence the moment of the weight of scale = 0
distance of force due to the weight of scale from the pivot = 10 cm (center of scale)
M = 2000 gf cm = F (10)
F = 200 gf
The weight of the meter scale= 200 gf .