. A heavy metallic scale of length 1 m has its centre of gravity at 50 cm division. It is suspended at a 30 cm mark. A load of 60 g wt has to be tied at its zero cm make to keep it in equilibrium. Calculate the weight of the scale.
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Answer :
- Weight of the metallic scale = 900 cm
Given :
• Length of the heavy metallic scale = 1 m
• The centre of gravity of scale = 50 cm
• Weight tied at zero cm mark = 60 g
To find :
• Weight of the scale
Figure :
To understand the question, firstly we'll make the figure. The length of the metallic scale is 1 m. Convert into cm.
→ 1 m = 100 cm
The length of the heavy metallic scale = 100 cm
Steps to draw the figure :-
- Draw a line and mark the end points as 0 cm and 100 cm.
- In the centre of the line mark 50 cm.
- Draw a downward arrow at 50 cm mark showing that the weight of the scale acts at that point.
- Draw a downward arrow at zero cm mark which represents that 60 g weight acts at the 0 cm mark.
- Make a small triangle at 30 cm mark representing the fulcrum.
Required Solution :
According to the law of moments,
The sum total of anticlockwise moments should be equal to the sum total of anticlockwise moments.
- A.C.W.D = C.W.D
⠀⠀⠀⇒ Let the weight of the scale be x
⠀⠀⠀⇒ 60 × 30 = (50 - 30) × x
⠀⠀⠀⇒ 1800 = 20 × x
⠀⠀⠀⇒ 1800 ÷ 2 = x
⠀⠀⠀⇒ 900 = x
⠀⠀⠀⇒ The value of x = 900
Therefore,
- The weight of the metallic scale = 900 g
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