(a) (i) Explain why x-rays can be used to produce photographs of fractures in bones.

(ii) List four uses of x-rays other than in medicine.

(b) State the energy transformations which takes place during the operation of an x-ray tube.

(c) (i) Explain three named dangers to which human beings may be exposed when subjected to large doses of x-rays.

(ii) State two precautions that must be taken by persons working with x-rays.

(d) In an x-ray tube, an electron is accelerated from rest towards a tungsten target biased at a potential of 33 kV. Calculate, for the electron, the

(i) kinetic energy;

(ii) velocity. [h = 6.6 x 10\(^{-14}\) Js; Me = 9.1 x10\(^{-31}\) kg; c = 3.0 x 10\(^4\) ms\(^{-1}\); e = 1.6 x 10\(^{-19}\) C.]

A spiral spring with a metal extends by 10.5 cm in air. When the metal is fully submerged in water, the spring extends by 6.8 cm. Calculate the relative density of the metal. (Assume Hooke's law is obeyed)

Study the diagrams above and use them as guides in carrying out the following instructions.

1. Using the spring balance provided, determine the weight of the object of mass M= 50.0g in air. Record this weight as W\(_{1}\).
2. Determine the weight of the object when it is completely immersed in water contained in a beaker as shown in the diagram above. Record the weight as W\(_{2}\).
3. Determine the weight of the object when it is completely immersed in a liquid labeled L. Record the weight as W\(_{3}\).
4. Evaluate U = (W\(_{1}\) - W\(_{2}\)) and V = (W\(_{1}\) -W\(_{3}\)).
5. Repeat the procedure with the objects of masses M= 100g, 150g, 200g, and 250g
6. In each case, evaluate U = (W\(_{1}\) - W\(_{2}\)) and V = (W\(_{1}\) -W\(_{3}\)).
7.  Tabulate your readings.
8. Plot a graph with V on the vertical axis and U on the horizontal axis.
9. Determine the slope, s, of the horizontal graph.
10. State two precautions taken to ensure accurate results.

(b)i. State Archimedes' principle.

ii.  A piece of brass of mass 20.0g is hung on a spring balance from a rigid support and completely immersed in kerosene from of density 8.0 x 10\(^{2}\)kgm\(^{-3}\).  Determine the readings of the spring balance (g= 10ms\(^{-2}\), density of brass 8.0 x 10\(^{3}\)kgm\(^{-3}\))

You are provided with a syringe, a petri-dish firmly attached to the base of the movable piston (plunger) of the syringe, a Set of weights, and other necessary apparatus.

1. Pull the piston of the syringe upward until it can no longer move. Read and record this position of the piston on the graduated mark on the syringe as V\(_{o}\).
2. Clamp the syringe and ensure that it is vertical.
3. Place a mass M= 500g gently at the center of the petri-dish.
4. Read and record the new position of the piston as V.
5. Evaluate V\(^{1}\).
6. Repeat the procedure for four other values of M= 1000g, 1500g, 2000g, and 2500g.
7. Tabulate your readings.
8. Plot a graph with V\(^{-1}\) on the vertical axis and M on the horizontal axis, starting both axes from the origin (0,0).
9. Determine the slope, s, of the graph.
10. Evaluate k = s\(^{-1}\).
11. State two precautions taken to ensure accurate results.

(b)i. When a weight is placed on the petri-dish, which quantities of the gas in the syringe (\(\Omega\)) increases; (\(\beta\)) decrease?

ii. What is responsible for the pressure exerted by a gas in a closed vessel?

You are provided with a potentiometer, an ammeter, a voltmeter, a standard resistor, and other necessary apparatus. Using the circuit diagram above as a guide carry out the following instructions.

1. Set up a circuit as illustrated in the diagram above.
2. Close the key, K.
3. Read and record the ammeter reading l\(_{o}\) and the voltmeter reading V\(_{o}\) when jockey J is not making contact with the potentiometer wire OQ.
4. Using J, make a contact with the potentiometer wire OQ at a point P such that OP = 1Ocm.
5. Read and record the current and the corresponding value of the voltage V.
6. Repeat the procedure for other values of OP= 20cm, 30cm, 40cm, 50cm, and 60cm.
7. Tabulate your readings.
8. Plot a graph with V on the vertical axis and I on the horizontal axis, starting both axes from the origin (0, 0).
9. Determine the slope, s, of the graph.
10. Determine the value of V when I = 0.
11. State two precautions taken to obtain accurate results.

(b) i. State two advantages of a lead-acid accumulator over a dry Leclanche cell.

ii. A cell of emf 2V and internal resistance of 1\(\Omega\) passes current through an external load of 9\(\Omega\). Calculate the potential drop across the cell.