Question

Find the weight of a metre scale balanced at 30cm mark such that two weights one of 80gf and 10gf are suspended at 5cm mark and 40cm mark respectively.​

Answer 1

The metre scale is balanced at 30 cm such that two weights one of 80 gf and 10 gf are suspended at 5 cm mark and 40 cm mark.

• Always remember that weight of the scale will act at the centre of mass (i.e. at the middle) at 50 cm mark.

• Also, the distance of force acting on the scale will be calculated from the 30 cm mark.

Now, since the scale is at rotational equilibrium, you can say:

$\sum( \tau) = 0$

$\implies  \{80 \times (30 - 5) \} = \{10 \times (40 - 30) \} +  \{w \times (50 - 30) \}$

$\implies  \{80 \times 25 \} = \{10 \times 10\} +  \{w \times 20 \}$

$\implies  2000 =20w + 100$

$\implies  20w  = 1900$

$\implies  w  = 95 \: gf$

So, weight of scale is 95 gf.

Answer 2

Draw the figure,mark the forces and show weight at 50 cm mark and apply the laws of moments