Question

A meter scale is supported on a wedge at its centre of gravity. A body of weight 'w' is suspended from the 20 cm mark and another weight of 25 gram is suspended from 74 cm mark balances it and the meter scale remains perfectly horizontal. Neglecting the weight of the meter scale, the weight of the body is

Answer 1

20 grams

Answer 2

For equilibrium, take moments about the pivot at the 50 cm mark (the centre of gravity).

• For the weight $w$ at 20 cm:

  Lever arm $= 50 - 20 = 30\, \text{cm}$

• For the 25 g weight at 74 cm:

  Lever arm $= 74 - 50 = 24\, \text{cm}$

Setting the clockwise moment equal to the anticlockwise moment:

$w \times 30 = 25 \times 24$

$w = \frac{25 \times 24}{30} = \frac{600}{30} = 20\, \text{g}$