Physics Past Paper form six NECTA 2017

SECTION A (40 Marks)
Answer any four (04) questions from this section.

MATANGAZO YA KAZI BOFYA HAPA

1: (a) Give the meaning of the following terms as used in error analysis:
(i) Absolute error. (01 mark)
(ii) Relative error. (01 mark)

(b) The force ‘F’ acting on an object of mass ‘m’, travelling at velocity ‘V’ in a circle of radius ‘r’ is given by; F = . If the measurements are recorded as: m =(3.5±0.1) kg, V = (20±1) m/s, r mV2 r = (12.5±0.5) m; find the maximum possible
(i) Fractional error. (03 marks)
(ii) Percentage error in the measurement of force. (02 marks)

2: (a) (i) Define the term dimensions of a physical quantity. (01 mark)
(ii) Identify two uses of dimensional equations. (02 marks)

b) (i) What is the basic requirement for a physical relation to be correct? (01 mark)
(ii) List two quantities whose dimension is [ML2T-1]. (01 mark)

(c) (i) The frequency ‘f’ of vibration of a stretched string depends on the tension ‘F’, the length ‘l’ and the mass per unit length μ of the string. Derive the formula relating the physical quantities by the method of dimensions. (03 marks)(ii) Use dimensional analysis to prove the correctness of the relation 𝜌 = , where by 𝜌 3g 4RG = density of the earth, g = acceleration due to gravity, R = radius of the earth and G gravitational constant. (02 marks)

3: (a) (i) Why does the kinetic energy of an earth satellite change in the elliptical orbit? (02 marks)
(ii) Give two factors which determine whether a planet has an atmosphere or not. (02 marks)

(b) A spacecraft is launched from the earth to the moon. If the mass of the earth is 81 times that of the moon and the distance from the centre of the earth to that of the moon is about 4.0×10 5 km;
(i) Draw a sketch showing how the gravitational force on the spacecraft varies during its journey. (03 marks)
(ii) Calculate the distance from the centre of the earth where the resultant gravitational force becomes zero. (03 marks)

4 (a) (i) Justify the statement that ‘If no external torque acts on a body, its angular velocity will not
be conserved’. (02 marks)
(ii) A car is moving with a speed of 30 ms-1 on a circular track of radius 500m. If its speed is increasing at the rate of 2ms-2; find its resultant linear acceleration. (03 marks)

(b) An object of mass 1kg is attached to the lower end of a string 1m long whose upper end is fixed
and made to rotate in a horizontal circle of radius 0.6m. If the circular speed of the mass is
constant, find the;
(i) Tension in the string. (03 marks)
(ii) Period of motion. (02 marks)

5 (a) A 75kg hunter fires a bullet of mass 10g with a velocity of 400ms-1 from a gun of mass 5kg.
Calculate the;
(i) Recoil velocity of the gun. (02 marks)
(ii) Velocity acquired by the hunter during firing. (03 marks)

(b) A jumbo jet travelling horizontally at 50ms-1 at a height of 500m from sea level drops a luggage of food to a disaster area.
(i) At what horizontal distance from the target should the luggage be dropped? (03 marks)
(ii) Find the velocity of the luggage as it hit the ground. (02 marks)

6 (a) The equation of simple harmonic motion is given as x = 6sin10𝜋t + 8cos10𝜋t, where x is in centimeter and t in second. Determine the;
(i) Amplitude. (03 marks)
(ii) Initial phase of motion. (02 marks)

(b) (i) Show that the total energy of a body executing simple harmonic motion is independent of time. (2.5 marks)
(ii) Find the periodic time of a cubical body of side 0.2m and mass 0.004kg floating in water then pressed and released such that it oscillates vertically. (2.5 marks)

SECTION B (30 Marks)
Answer three (03) questions from this section.

7 (a) (i) Give a common example of adiabatic process. (01 mark)
(ii) What happens to the internal energy of a gas during adiabatic expansion? (02 marks)

(b) A mass of an ideal gas of volume 400cm3 at 288K expands adiabatically. If its temperature falls
to 273K;
(i) Find the new volume of the gas. (02 marks)
(ii) Calculate the final volume of the gas if it is then compressed isothermally until the pressure returns to its original value. (04 marks)

8 (a) State the following according to heat exchange:
(i) Prevost’s theory. (1.5 marks)
(ii) Wien’s displacement law. (1.5 marks)

(b) Briefly explain why;
(i) Steam pipes are wrapped with insulating materials? (1.5 marks)

(ii) Stainless steel cooking pans fitted with extra copper at the bottom are more preferred? (1.5 marks)
(c) The value of the property X of a certain substance is given by; X𝜃 = X𝜎 0.5𝜃 + 2 × 10-4𝜃 2
, Where 𝜃 is the temperature in degrees celsius. What would be the celsius temperature defined by the property X which corresponds to a temperature of 50°C on this gas thermometer scale? (04 marks)

9 (a) (i) What is the advantage of using a greater length of potentiometer wire? (02 marks)
(ii) Why is a Wheatstone bridge not suitable for measuring very high resistance? (02 marks)