Section A
i.Answer all questions in this section.
ii.Write down answers in the spaces provided in this question/answer book. In calculations you should show all the main steps in your working.
iii.Assume:velocity of light in air = 3 x 108ms-1
acceleration due to gravity = 10 ms-2
1.Figure 1.1 shows a smooth box in which a small block of mass m is connected by two identical light springs to opposite sides, A and B of the box.
Initially both springs are stretched an equal amount e and force constant is 10Nm-1 each. Then the box is tilted at an angle of 30o to the horizontal. The block reaches its equilibrium position when it moves 2cm down the surface of the box.
Now the block is displaced 1cm from the equilibrium position and released from rest (Assume that both springs are always in tension).
(a)(i)Calculate the mass of the block.(1 mark)
(ii)Show that the motion of the block is simple harmonic.(4 marks)
(b)Now a plasticine of 1kg is carefully placed on the block when the block passes the equilibrium position. Calculate the new amplitude after the landing of the plasticine. (4 marks)
(c)If the box is tilted through a larger angle, would you expect the period of the oscillation will increase, decrease or remain unchanged? Explain your answer. (3 marks)
2.
The graph in Figure 2.1 shows a simplified model of the attractive and repulsive forces between two atoms plotted against their distance of separation.
(a)Explain briefly why there are attractive force and repulse force existing between atoms. (2 marks)
(b)Draw the resultant force on the figure 2.1.(2 marks)
(c)Estimate on the graph the equilibrium separation between the atoms. Explain its significance in term of potential energy of the atoms. (2 marks)
(d)A material is made up of atoms shown in figure 2.1, estimate from the graph,
(i)the energy required to separate two atoms completely from equilibrium position. (2 marks)
(ii)the Young’s modulus(2 marks)
(iii)the breaking stress(2 marks)
of the solid.
3.One mole of helium gas undergoes a cycle ABCA in which its pressure, P and
temperature T are indicated in the P-T diagram in the figure 3.1.
Given: Universal gas constant = 8.31 J mol-1 K-1
Avogadro constant = 6.02 x 1023 mol-1
Assume that helium gas behaves as an ideal gas.
(a)(i)Find the volume of the gas at state A.(2 marks)
(ii)Calculate the root mean square speed of the helium gas at state A.
(2 marks)
(iii)Do you expect the value calculated in (ii) would be higher or lower, if the gas is oxygen gas of same mole? Explain briefly. (3 marks)
(b)(i)Draw a relevant P-V graph corresponding to the cycle ABCA.
(3 marks)
(ii)Calculate the net work done by the gas in the cycle ABCA.
(2 marks)
4.
(a)In an experiment with an illuminated photocell, a small current is detected by the microammeter even when the anode is made slightly negative with respect to the cathode, using the circuit of Figure 4.1. Briefly account for this. (2 marks)
(b)By adjusting the potential between the cathode and anode, the photoelectic current varies as shown in the figure 4.2.
Given:Planck constant = 6.63 x 10-34 Js
Charge of an electron = 1.60 x 10-19 C
(i)What is the significance of the point X in the graph?(2 marks)
(ii)If X is -2.67V, what is the maximum kinetic energy of the photoelectrons emitted? (2 marks)
(iii)If the work function of the metal is 2.3eV, what is the wavelength of the incident ray? (2 marks)
(c)Curve A is shown again in Figure 4.3. Sketch the form of the curve you would expect to obtain if
(i)light of the same intensity but higher frequency were used. Label your curve B.
(ii)light of the same frequency but lower intensity were used. Label your curve C.
(4 marks)
5.(a)What is meant by the moment of inertia?
What is its significance of a rigid body in rotational motion?(2 marks)
(b)A hollow sphere A of mass 1 kg rolls down without slipping along the inclined plane.
The external diameter of the sphere A is 10 cm. The sphere rolls down at a height of 0.5m. It has a velocity of 2.54 ms-1 when it reaches the bottom of the plane.
(i)What is the work done against friction during the journey?
(1 mark)
(ii)Considering the energy conservation, write an expression for the moment of inertia I and hence find the value of I.
(3 marks)
(c)Another solid sphere B of mass 2.05kg of the same diameter and material as sphere A rolls down at the same height. It is found that it has a speed of 2.67 ms-1 when it reaches the bottom.
(i)Calculate the density of the sphere B.(1 mark)
(ii)Calculate the moment of inertia of sphere B.(1 mark)
(d)By using the results in (b) and (c), find the moment of inertia of a solid sphere of diameter 8 cm made from the material same as sphere A and B.
(4 marks)
2000-AL-PHY IA-1