A uniform metre scale balances horizontally on a knife edge placed at the 58 cm mark when a mass of 20g is suspended from one end.
(i) Draw a diagram of the arrangement and (ii) Find mass of the metre scale.
Answer/Solution:
Let, W be the mass of uniform scale,
When the edge is placed at 58 cm mark and 20 g weight suspended at one end, then uniform scale would be balaced.
Applying here the principle of moments:
The uniform scale weight would be balanced at mid point i.e. 50 cm of the scale.
A weight of 20 g is placed at 58 cm mark.
So the clockwise moment due to mass of the scale will be W(50-42) = 8W
The anticlockwise moment due to mass 20g will be 20*(50-8) = 840.
For equilibrium, clockwise moment = anticlockwise moment
So,
W x 8 = 840
W = 105 g
The wight of the uniform meter = 105 g.
Diagram is:
Let, W be the mass of uniform scale,
When the edge is placed at 58 cm mark and 20 g weight suspended at one end, then uniform scale would be balaced.
Applying here the principle of moments:
The uniform scale weight would be balanced at mid point i.e. 50 cm of the scale.
A weight of 20 g is placed at 58 cm mark.
So the clockwise moment due to mass of the scale will be W(50-42) = 8W
The anticlockwise moment due to mass 20g will be 20*(50-8) = 840.
For equilibrium, clockwise moment = anticlockwise moment
So,
W x 8 = 840
W = 105 g
The wight of the uniform meter = 105 g.
Diagram is: