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Grade 12th PassMechanics

a uniform metre scale of mass 1kg is placed on table such that a part of the scale is beyond edge.if a body of mass 0.25kg is hung at the end of the scale then the minimum length of scale on table so that it doesnt tilt?

Prakhar

10 Years agoGrade 12th Pass

1 Answer

Riddhish Bhalodia

10 Years ago

This is a standard torque balancing problem

Lets say length L is the minimum length on the table that will balance the scale
now think of this 2 masses of L kg and (1-L)kg, on the table and outside the table respectively

Draw the FBD and you will see when we balance torque about the hinge point we get
$Lg \times L/2 = 1/4g\times (1-L) + (1-L)g\times(1-L)/2$
$2L^2 = (1-L) + 2(1-L)^2 = 2L^2 -5L + 3$
$-5L + 3 = 0, \Rightarrow L = 3/5$

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