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**Finding the mass and weight of uniform body**

When body is uniform, the mass or weight must act at the centre. A metre rule is marked from 0-100cm mark. If it is uniform, then its mass/weight must act in the middle, which is 50cm mark.

The mass or weight is calculated by applying the principle of moment.

**Example 2:**

A metre-rule suspended from the centre of gravity is in equilibrium, i.e balanced at G, when forces ofW1, W2 and W3, act at distances of a, b and c respectively from the pivot.

(i) Draw a labeled diagram to show all the forces acting on the metre-rule.

(ii) Write an expression for the sum of the moments.

Taking moments about the pivot;

Sum of Anticlockwise moments = W1× d1+W2× d2

Sum of Clockwise moments = W3×c

Applying the principle of moments; Sum of clockwise moments = Sum of anticlockwise moments

W3× c = W1× a + W2×b

**Example3:**

A uniform metre rule is pivoted at its centre and three forces of 6N, 2N and F act at distances of 20cm, 60cm, and 80cmrespectively from the zero mark. If the metre rule balances horizontally, find the value of F.

**Solution**

Taking moments about the pivot; Sum of Anticlockwise moments =6×30 = 180Ncm Sum of Clockwise moments =2×10+F×30

=(20+30F) Ncm

Applying the principle of moments; Sum of clockwise moments = Sum of anticlockwise moments (20+30F) Ncm =180Ncm 30F =160

F =5.3 N

**Example 4:**

A non-uniform tree trunk of weight 1000N is placed on a pivot, 4m from the thick end. A weight of 800N is placed on the other side of the pivot, at a distance equal to that from the thick end to the centre of gravity, just tips off the tree trunk. How far is the weight from the thick end?

**Solution:**

Let the distance from the thick end to the Centre of gravity (C.O.G) be x.

Taking moments about the pivot;

**Example: 1**

A uniform metre rule is suspended from 40cm marking as shown in the diagram below. Find the mass of the metre rule if it’s in equilibrium.

Taking moments about the pivot;

𝒙=(40−10)=30𝑐𝑚

𝒅=(50−40)=10𝑐𝑚

**Example 2:** A uniform metre rule pivoted at 10cm mark balance when a mass of 400g is suspended at 0cm mark. Calculate the mass of the metre rule.** (Ans: m=100g)**

**Example 3: **The diagram below is a metre rule pivoted at 80cm mark. Calculate the mass of the metre. **(Ans: m=67g)**

**Example 4: **A uniform beam 2m long is suspended as shown below. Calculate the mass of the metre. **(Ans: m=16kg)**