A uniform metre rule rests horizontally on a knife edge at the 60cm mark when a mass of 10g is suspended from one end. Draw a diagram of the arrangement. (a) At which end must this mass be suspended (b) What is the mass of the rule? (c ) THe 10g mass is now shifted to the 90cm mark. In which direction must the knife edge be shifted to make the rule horizontal again?

A uniform metre rule rests horizontally on a knife edge at the 60cm ma

1.	A uniform metre rule rests horizontally on a knife edge at the 60cm mark when a mass of 10g is suspended from one end. Draw a diagram of the arrangement. (a) At which end must this mass be suspended (b) What is the mass of the rule? (c ) THe 10g mass is now shifted to the 90cm mark. In which direction must the knife edge be shifted to make the rule horizontal again?
Answer» Solution :(a) Fig. 1.22 shows a UNIFORM metre rule ABwhich rests horizontally on the knife edge at O (60 cmmark). Let Mg be the mass of the rule . A uniform rule has same distribution of mass throughout its length, so its weight Mg will act at its middle point i.e., at the 50cm MARK. The weight Mg of the rule PRODUCES an anti-clockwise moment about the knife edge O. In order to BALANCE it, 10g mass must be suspended at the end B (i.e., at the mark 100cm) to produce a clockwise moment about the knife edge O. (b) From the principle of moments Anticlockwise moment= Clockwise moment `Mg times (60 -50)=10g times (100-60)` or `Mg times 10=10 g times 40` `therefore` Mass of rule M=40g When the 10g mass is shifted to the 90cm mark, its distance from the knife edge reduces resulting in decrease of clockwise moment. SO the knife edge must be shifted away from the 10g mass to reduce the distance between the knife edge and mass M so as to make the anticlockwise moment byM equal to the reduced VALUE of clockwise moment.