Question

A uniform metre scale is kept in equilibrium when supported at the 60 cm mark and a mass M is suspended from the 90 cm mark as shown in the figure. State with reasons, whether the weight of the scale is greater than, less than or equal to the weight of mass M.

The figure shows a uniform metre scale in the equilibrium position. State with reason if the weight of the scale is more than, equal to or less than the weight of mass M.

Answer 1

Let M be load.
∴ Load arm = 90 – 60 = 30 cm
Since wt. of scale will act at centre of gravity of scale which is the midpoint of the scale.
∴ Effort arm = 60 – 50 = 10 cm
Let wt. of scale be W
By principal of moments L × d_L = E × d_E
M × 30 = W × 10
W = 3M
∴ Since the weight of scale is three times that of M.
∴ The weight of the scale is greater than the weight of M.