Question

a metre scale is kept on a knife edge at 50 cm mark. a weight of 20gf is hanging at 80 cm mark and a weight of 50gf is hanging at 60cm mark. Where should a weight of 55gf be placed to make the metre scale balanced?​

Answer 1

Given :

Weight at 80 cm mark = 20gf

Weight at 60 cm mark = 50 gf

To find :

To balance the scale , the mark where the 55 gf of weight should be placed .

Solution :

Let the mark be x where 55gf is hanging .

There will be a tendency of rotation in the scale .

Let the velocity be v , with which the tendency of rotation will be there .

by conservation of angular momentum ,

    20 * v * (80 - 50) + 50 * v * (60 - 50) = 55 * v * ( 50 - x )

=> 20 * 30 + 50 * 10 = 55 * ( 50 - x )

=> 1100 = 55 * ( 50 - x )

=> 50 - x = 20

=> x = 30

The weight of 55gf should be placed at 30 cm mark to make the metre scale balanced .