A uniform half metre rule can be balanced at the 29.0 cm mark when a mass 20g is hung from its one end.

(a) Draw a diagram of the arrangement.

(b) Find the mass of the half metre rule.

(c) In which direction would the balancing point shift if 20g mass is shifted inside from its one end?

A uniform metre rule of mass 100 g is balanced on a fulcrum at mark 40 cm by suspending an unknown mass m at the mark 20 cm.

(i) Find the value of m.

(ii) To which side the rule will tilt if the mass m is moved to the mark 10 cm?

(iii) What is the resultant moment now?

(iv) How can it be balanced by another mass 50 g?

The centre of gravity of a body is the point about which the algebraic sum of moments of weights of all the particles constituting the body is:

1. 1
2. > 1
3. < 1
4. 0

The centre of gravity of a hollow cone of height h is at distance x from its vertex where the value of x is:

1. $\dfrac{\text{h}}{3}$
2. $\dfrac{\text{h}}{4}$
3. $\dfrac{2\text{h}}{3}$
4. $\dfrac{3\text{h}}{4}$