Question

A uniform meter scale of mass 1kg is placed on a table such that a part of the scale is beyond the edge. If a body of mass 0.25 kg is hung at the end of the scale, then the minimum length of scale that should lie on the scale that should lie on the table so that it does not tilt is?

Answer 1

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Answer 2

Explanation:

Given A uniform meter scale of mass 1 kg is placed on a table such that a part of the scale is beyond the edge. If a body of mass 0.25 kg is hung at the end of the scale, then the minimum length of scale that should lie on the scale that should lie on the table so that it does not tilt is?

• Let a scale be placed on a table. A part is beyond the table. Let AB be the length of table and AC be the  part of the edge. So the mass that is hung is 0.25 kg. The mass of table works at the midpoint of table since it is uniform and the centre will be 1 m. The mass of meter scale is 1kg. Question is the length that lies on the table. We need to find BC.
• Suppose AC = x
• Now going from the verge condition that suppose it is tilted,the scale will start loosing contact and there will be a reaction force. So the end force will be 0.25 x g and midpoint of table will be 1 x g, so there will ne force.
• At the transitional equilibrium, net force is zero and in rotational equilibrium, net moment is zero.
• At the equilibrium, taking moment at point c we have, one is clockwise and another will be anticlockwise. So clockwise is positive and anticlockwise is negative.
•           So – 0.25 x x + 1 x g (0.5 – x) = 0
•          So x = 50 / 1.25
•                  = 40 cm
• So BC = 100 – 40 (1 m = 100 cm)
• Or BC = 60 cm

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