Question
Download Solution PDFA uniform meter scale weighs 50 g. It is pivoted at the 70 cm mark. Where should a 40 g mass be placed so that the scale is in equilibrium?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Principle of Moments:
- If the algebraic sum of moments of all the forces acting on the body about the axis of rotation is zero, the body is in equilibrium.
- According to the principle of moments, in equilibrium: The sum of anticlockwise Moments = Sum of clockwise moments.
Calculation:
Given:
Meter scale, i.e. length of scale = 100 cm, weight of scale = 50 g
Let x be the required distance from the pivoted end. Then as the meter scale is uniform, its weight will act at its midpoint, i.e., the 50 cm mark. The mass of the meter scale produces an anticlockwise moment about O and the suspended weight produces a clockwise moment.
Anticlockwise moment of the weight of the scale about O = 50 × (70 - 50) = 50 × 20
Clockwise moment of mass 40 g about O = 40x
According to the principle of moments,
Anticlockwise moment = Clockwise moment
⇒ 50 × 20 = 40x
⇒ x = 25 cm
∴ 40 g mass should be placed at (70 + 25) = 95 cm so that the scale is in equilibrium
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