Question

A uniform half-meter rule balances horizontally on a knife-edge at the 29 cm mark when a weight of 20 gf is suspended from one end.

What is the weight of the half-meter rule?

Answer 1

Step 1: Assumptions made for the solution

Let the weight of the half-meter rule be w.

The length of the half-meter rule is 50 cm.

The center of gravity of a uniform half-meter scale = $\frac{50\mathrm{cm}}{2}=25\mathrm{cm}$

Step 2: Explanation of the quantities

The ruler balances horizontally on a knife-edge at 29 cm mark.

So the distance between the center of gravity and the balance point, $\mathrm{a}=\left(29-25\right)=4\mathrm{cm}$

The distance between the knife edge and the weigh, $\mathrm{b}=50-29=21\mathrm{cm}$

The weight suspended from one end $\mathrm{W}=20\mathrm{gf}$

Step 3: Calculation of weight of the half-meter ruler

As the ruler is in balance condition, therefore,

$$\begin{gathered} \mathrm{w}\times \mathrm{a}=\mathrm{W}\times \mathrm{b} \\ \mathrm{w}=\frac{\mathrm{W}\times \mathrm{b}}{\mathrm{a}} \\ \mathrm{w}=\frac{20\mathrm{gf}\times 21\mathrm{cm}}{4\mathrm{cm}} \\ \mathrm{w}=\frac{420}{4} \\ \mathrm{w}=105\mathrm{gf} \end{gathered}$$

Step 4: Final answer

So, the weight of the half-meter rule is 105 gf.