Question

A one-meter scale AB is balanced horizontally across a knife-edge as shown in the figure.

Calculate the mass of the scale

Answer 1

Step 1: Given data

Length of the scale = 100 cm

Mid-point of the scale = 50 cm

The distance between the knife edge and 50g weight = 30 cm

Weight at point A = 50g

Let the mass of the scale is w.

Step : Calculating the mass of the scale

Moment of force $\tau =F\times d$ where F is the force, d is the perpendicular distance of line of action of force from the axis of rotation

The sum of the anticlockwise moment on the left arm = The sum of the clockwise moment on the right arm

$$\begin{gathered} Torque,\tau =F\times d \\ \mathrm{Force}\mathrm{on}\mathrm{the}\mathrm{left}\mathrm{arm}\times \mathrm{distance}\mathrm{from}\mathrm{the}\mathrm{fixed}\mathrm{axis}\mathrm{for}\mathrm{left}\mathrm{arm}=\mathrm{Force}\mathrm{on}\mathrm{the}\mathrm{right}\mathrm{arm}\times \mathrm{distance}\mathrm{from}\mathrm{the}\mathrm{fixed}\mathrm{axis}\mathrm{for}\mathrm{right}\mathrm{arm} \\ \mathrm{w}\times \left(50-30\right)\mathrm{cm}=50\mathrm{g}\times \left(100-30\right)\mathrm{cm} \\ \mathrm{w}\times 20cm=50g\times 70cm \\ \mathrm{w}=\frac{50g\times 70cm}{20cm} \\ \mathrm{w}=\frac{3500}{20} \\ \mathrm{w}=175\mathrm{g} \end{gathered}$$

Step 3: Final answer

So, the mass of the scale is 175 g.