Physics Paper 3 Questions and Answers with confidential - Form 3 End Term 1 Exams

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INSTRUCTIONS TO CANDIDATES

Answer ALL the questions
You are supposed to spend the first 15 minutes of the 2 1/4 hours allowed for this paper reading the whole paper carefully before commencing your work.
Marks are given for clear record of observations made, their suitability, accuracy and the use made of them.
Candidates are advised to record their observations as soon as they are made.
Non-programmable silent electronic calculators and KNEC mathematical table may be used.

PART A

You are provided with the following:
- A retort stand, clamp and boss.
- A spiral spring.
- A stop watch.
- Three 100g masses.
- Three 50g masses.
  
  PROCEDURE
  1. Suspend a 100g mass at the end of a spiral spring as shown below.
  2. Now give the mass a small vertical displacement and release so that it performs vertical oscillation.
  3. Time for 20 oscillations and determine the period.
    Enter the result in the table below.
  4. Repeat the experiment for other values of mass given and complete the table.
    
    Mass m(g) 100 150 200 250 300 350
    
    Time for 20 oscillations t (s)
    
    Period time T (s)
    
    T² (S²)
    
    6marks
  5. Plot a graph of T² (S²) (y –axis) against m (kg). (5marks)
  6. Determine the slope of the graph. (2marks)
  7. Given that T^2=2mwhere k is the spring constant , use the graph to obtain the value of the spring constant k. (2marks)
    
    PART B
    
    You are provided with the following
    - 5 optical pins
    - A rectangular glass block
    - A plain paper
    - A soft board
    - 4 thumb pins
      
      Proceed as follows
  8. Fix the white piece of paper on the soft board using thumb pins. Place the glass block on the white paper and draw the outline of the block.
  9. Remove the glass block and indicate the sides A, B, C and D as shown.
  10. On side BC, determine its center and fix a pin P₀ as shown. Looking from one side at the opposite end of the slab, fix pin P₁ and then pin P₂ so that they are in line with the image I of the pin P₀ .On the other side locate the same image using pins P₃ and P₄ as shown above.
  11. Remove the glass block and the pins and produce lines P₁P₂ and P₃P₄ to their points of intersection; (the position of the image I) (1mark)
  12. Determine the midpoint of AD and label it Q. Measure the lengths QP0 and Q1. (2marks)
    QP₀ =..............................cm
    Q1 =.................................cm
  13. Work out the ratio =QP_O =n (1mark)
    Q1
  14. What does n represent (1mark)

You are provided with the following;-

two retort stands
a metre rule
some cotton thread (approximately 1.2m long)
a ball of plasticine
a stop watch
a protractor

half metre rule

Proceed as follows:

Attach one end of a string to the metre rule at 10cm by fastening a loop of string tightly round the metre rule. Fix the string at this point with a small piece of plasticine. Tie the other end of the string around the metre rule at the 90cm mark. Fix this loop with another small piece of plasticine.
Attach the pendulum bob to the centre of the string so that the centre of gravity of the bob is 15.0cm below the point of suspension (see figure below)

marks: refix the plasticine
measure the angle 2Ө and period T, as before.
Repeat (ii) above with the loops at 15cm and 85cm, 20cm and 80cm, 25cm and 75cm , 30cm and 70cm, 35cm and 65cm

Enter all your results in the table below: (7mks)

Position of loop	2θ	Cos θ	Time , t for 10 oscillations	Period, T (sec)	T²(S²)
10cm and 90cm
12cm and 88cm
15cm and 85cm
20cm and 80cm
25cm and 75cm
30cm and 70cm
35 cm and 65cm

1. On the grid provided plot a graph of T²(S²) (y-axis) against Cosθ (5mks)
2. Find the intercept on the T²-axis (1mk)
3. Determine the slope of your graph (2mks)
1. Measure the angle 2θ
2. Pull the pendulum towards you through a small distance, releases it and measure the period, T for motion by timing 10complete oscillations
3. Remove the pasticine slide the loops to the 12cm and 88cm
1. Measure the length, L, of the pendulum when 2θ= 0° in metres (1mk)
2. From your graph, determine the period T of the pendulum when
  2θ = 0° (2mks)
3. Using the formula T =2π^l/_g determine the value of ‘g’ given that T= 2.0 (2mks)

Marking Scheme

Mass m(g)	100	150	200	250	300	350
Time for 20 oscillations t (s)	6.59	8.03	9.60	10.91	11.57	12.56
Period time T (s)	0.3295	0.4015	0.4800	0.5455	0.5785	0.6280
T² (S²)	0.1086	0.1612	0.2304	0.2976	0.3347	0.3944

For t each correct value ½mk max 3mks
For T all values correct 2mks more than 3 correct
1mk less than three correct 0mk. max 2mks
For T² all values correct 1mk max 1mk

Gradient = ∆Y = ∆T² = 0.25-0 ✔1 =1.111 s²/kg ✔¹
∆X ∆m 0.225-0
y = mx +c
T²=π² M+0 =Slope=π²
K K
K= π² ✔ = π² = 8.972N/m ✔
slope 1.11
Lines P₁P₂ & P₃P₄ intersecting at I ✔
QP₀ = 10.0cm✔
Q₁= 6.6 cm✔
n = QP₀ = 10.0 = 1.5152✔
QI 6.6
Refractive index✔

Position of loop	2θ	θ	Cos θ	Time , t for 10 oscillations	Period, T (sec)	T²(S²)
10cm and 90cm	165°	82.5°	0.1305	0.917	0.917	0.841
12cm and 88cm	133°	66.5°	0.3987	1.135	1.135	1.288
15cm and 85cm	120°	60°	0.50	1.190	1.190	1.416
20cm and 80cm	97°	48.5°	0.6626	1.303	1.303	1.698
25cm and 75cm	78°	39°	0.771	1.370	1.370	1.877
30cm and 70cm	60°	30°	0.8660	1.420	1.420	2.016
35 cm and 65cm	45°	22.5°	0.9239	1.470	1.470	2.161

1. Plotting – atleast 5pts correctly plotted (2mks)
  3 or 4 pts (1mk)
  Axes 1mk
  Scale 1mk
  Line(1mk
2. Intercept – 0.63, 0.252(1mk)
3. Gradient =
1. L=0.55m
  T² = 2.2s²
  T = 1.483s
2. T=2π^l/_gT² = 4π². ^l/_g2.2 = 0.55 x 4π²
  g
  g=9.87