A uniform metre rule of mass 100g is balanced on a fulcrum at mark 40cm by suspending an unknown mass m at the mark 20cm.
(i) Find the value of m.
(ii) To which side the rule will tilt if the mass m is moved to the mark 10cm?
(iii) What is the resultant moment now?
(iv) How can it be balanced by another mass of 50 g?

Explanation

To solve the problem step by step, we will break it down into parts as outlined in the question.

### Part (i): Find the value of m.

1. **Identify the forces and distances:**
- The mass of the meter rule (uniform) is \(100 \, \text{g}\) and its center of mass is at \(50 \, \text{cm}\).
- The fulcrum is at \(40 \, \text{cm}\).
- An unknown mass \(m\) is suspended at \(20 \, \text{cm}\).
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