Two radioactive elements A and B have half-lives of 100 and 50 years respectively. Samples of A and B initially contain equal amounts/number of atoms. What is the ratio of the number of the remaining atoms of A to that of B after 200 years?

During the same interval, it is observed that a train travels the same distance as does a lorry. The two vehicles therefore have the same

(a) Explain with the aid of a diagram what is meant by the moment of a force about a point.

(b) State the conditions of equilibrium for a number of coplanar parallel forces. 

A metre rule is found to balance at the 48cm mark. When a body of mass 60g is suspended at the 6cm mark, the balance point is found to be at the 30cm mark. Calculate:

(i) the mass of the metre rule; (ii) the distance of the balance point from the zero end, if the body were moved to the 13cm mark.

(c) Show that the efficiency E, the force ratio M.A and the velocity ratio V.R of a machine are related by the equation \(E = \frac{M.A}{V.R} \times 100%\)

The efficiency of a machine is 80%. Determine the work done by a person using this machine to raise a load of 200kg through a vertical distance of 3.0m.

[Take g = 10ms\(^{-2}\)]

(a) Draw a labelled diagram of a vacuum flask. Explain how its construction minimizes heat exchange with the surroundings.

(b) State Boyle's law. A thread of mercury of length 15cm is used to trap some air in a capillary tube with uniform cross- sectional area and closed at one end with the tube vertical and the open end uppermost, the length of the trapped air column is 20cm. Calculate the length of the air column when the tube is held:

(i) Horizontally ; (ii) vertically with the open end underneath. [Atmospheric pressure = 76cm Hg]

(c) Explain why it is not advisable to sterilize a clinical thermometer in boiling water at normal atmospheric pressure.