The uncertinty in determining the duration during which an electron remains in a particular energy level before returning to the ground state is 2.0 x 10\(^{-9}\)s. Calculate the uncertainty in determining its energy at that level [Take \(\frac{h}{2\pi} = h = 1.054 \times 10^{-34}\) Js]

A paralIel beam of unpolarized light is incident on a plane glass of refractive index 1.60 at an angle to the normal. If the reflected beam is completely polarized, calculate the angle of incidence of the beam.

List three observations in support of the de-Broglie's assumptions that moving particles behave like waves.

(a) State two;

(i) laws of solid friction;

(ii) advantages of friction;

(iii) methods of reducing friction.

(b) Draw and label a diagram of a pulley system with velocity ratio of 5.

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

(ii) The efficiency of a machine is 80%. Calcuate the work done by a person using the machine to raise a load of 300 kg through a height of 4 m.[ g = 10 ms\(^{-2}\) ]

(a) With the aid of ray diagrams, explain total internal reflection.

(b) Describe, with the aid of a labelled diagram, the essential features of an astronomical telescope in normal adjustment.

(c) A converging lens forms a real image of a real object. If the magnification is 2 and the distance between the image and the object is 90.0 cm, determine the

(i) focal length of the lens;

(ii) object distance for which the image would be the same size as the object.