CIE 9702 Physics Paper 43 ON 2015 Mark Scheme Answers

  

  9702/43/O/N/15

Q1(a)

Gravitational force between two point masses is directly proportional to product of their masses and inversely proportional to square of their separation.

Note: The law can only be applied on mass of a single dot in space. Alternatively, you can comment that the size of the objects is much less than their separation.

Q1(b) 

Gravitational force provides the centripetal force 

GM m / r² = m r ω² where r is equivalent to x

GM =  r³ (2π / T)² 

leading to the answer

Note: State the physics concept from which you derive the equation. Comment on 'r' if it is used instead of 'x'

Q1(c) 

GM = 4 π² x³ / T²

  M = 4 π² x³ / GT²

        = 4 π² (4.5 x 10¹⁴ x 10³) / (6.67 x 10^-11)(0.35 x (24 x 60 x 60)² )

Note: Must draw in the graph the extrapolation to the origin, only then allowed to substitute value of a single point. Otherwise, gradient method shall be shown. 

This question involves massive substitution of values, make sure you double check.

Must convert 'g' to 'kg' and 'day' to 's'

---

Q2(a)

- negligible inter-molecular force
- negligible total volume of molecules compared to the volume of the container
- negligible impact time with the wall of the container

Note: The question has given one, i.e. consist of molecules that are 'elastic'. Repeating the point of elastic collision score no mark. 

(b) 

speed, v² is replaced with mean square of speed, <c²>, because molecules in a gas will not have the same speed.

(c) (i)

           p = 1/3 n m <c²>

1.2 x 10⁵ = 1/3 (1.2) <c²>

<c²> = 3.0 x 10⁵

root of  <c²> = 548 m s^-1

(c) (ii)

From 1/2 m <c²> = 3/2 k T

<c²> is directly proportional to T (in kelvin)

<c²>/ (3.0 x 10⁵) = (207+273) / (27+273)

<c²> = 4.80 x 10⁵  m s^-1

---

Q3(a)

Thermal equilibrium is a state when the two bodies are at the same temperature. There is no net transfer of thermal energy between them

Note: Avoid saying the two bodies have constant temperature. Specify that the energy as thermal energy.

Q3(b) (i)

 57.2 - 15.9 = 41.3 K

(b) (ii) 
57.2 + 273.15 = 330.4
Note: Use least dp, i.e. 1 dp. 

(c)
change in U = change in Q + change in W
   internal energy only consist of Ek
   constant pressure means, volume directly proportional to temperature,
   since temperature increases, volume will increase, so work is done by gas
change in Ek = change in Q - work done by gas
change in Q = increase in Ek + work done by gas
                     = 3/2 (1.9)(41.3) + (1.2 x 10⁵)(950 x 10^-6)
                     = 171 + 114
                     = 285

---

Q4(a)

Simple harmonic motion is an oscillatory system where the acceleration is directly proportional to its displacement, and it is always opposite in direction with the displacement.
Note: You can also describe that the acceleration is always directed towards the equilibrium position

(b)
The tube floats, means upthrust balances its weight
ρ g A h = mg
0.79 x (10^-3 / 10^-6) x 4.9 x 10^-4 x h = 0.070
h = 0.18 m

(c) (i) 1.
t₁ = half of period
4π² / T² = ρ A g / M
               = 0.79 x (10^-3 / 10^-6) x 4.9 x 10^-4 x 9.81 / 0.070
T = 0.85 s
t₁ = 0.43 s

(c) (i) 2.
t₃ = 3 x t₁ = 1.29 s

(c)(ii)
h of t₁ = 2.2 cm , h of t₂ = 1.0 cm
energy of peak = ½ M ω² x₀²
Lost = ½ M ω² (x₀₁² - x₀₂²) 
        = ½ (0.070) ( 4π² / 0.85²) ( 0.022²  - 0.010² )
        = 7.34 x 10^-4 J

---

Q5(a)

Charges are stationary inside metal. The resultant force on these charges is zero. 

Note: Question said: suggest why, not use Fig 6.1 to..., therefore you can give situation where it is evident that E is zero.

However, 1 mark might be awarded for using the evidence from Fig 6.1, e.g. the graph shows that the value of E is zero inside the metal sphere.

Q5(b)

V at 7.0 cm = 28.0 x 0.07 = 1.96 V

V at 5.0 cm = 54.0 x 0.05 = 2.70 V

Change in potential energy = q x (change in V)

                                            = 8.5 x 10^-9 x (2.70 - 1.96)

                                            = 6.3 x 10^-9 J

Note: The idea of the method shown above is: calculate the potential at each x, then find the potential difference, then multiplied by q, to determine the change in potential energy.

---

Q6(a)

A straight current-carrying conductor generates magnetic fields around it. The direction of the magnetic field can be determined using Right Hand grip rule. Since the current in the top and the bottom wires have the same magnitude and are in opposite direction, the direction of magnetic field will also be in the opposite direction, and will cancel out. Therefore zero resultant field..

Q6(b)
As the iron core brought near to the solenoid, it will be magnetized, creating an increasing magnetic field. This changing magnetic fields cut through the solenoid. According to Faraday's law, this will induce an emf in the solenoid.
But according to Lenz's Law, this emf will oppose the increasing the magnetic fields, by creating opposite magnetic fields. To create opposite fields, its' direction will have to be opposite to the  emf of the battery.
Note: It is not a magnet that is approaching the solenoid. 

---

Q7(a)

(i)

Vo = √2 x 14 = 19.8 V

(ii)

ω = 2 π (750) = 4700 rad s^-1

(b)

Capacitance is ratio of charge to p.d.. Capacitor with large capacitance can store more charge on one of the capacitor plate, and capacitor usually charge and discharge very quickly. This means large amount of charge flow in a short time. So it may draw large current from the supply.

Note: This is a conceptual question, that can be explained using simple physics. There is no need to memorize the answer. 

---

Q8(a)

hc / λ = φ + E_MAX, h = planck's constant ; c = speed of light in vacuum

(b)

(i)

gradient of the graph = hc. 

Since h and c are both constants, the gradient is independent of metal surface.

(ii)When E_MAX is zero,

 = hc (1/λ_o)

2.28 x 1.6 x 10^-19  = 6.63 x 10^-34 x (3.00 x 10^-8) / λ_o

                            λ_o  = 5.45 10^-7 m  

---

Q9(a)

Binding energy is the amount of energy needed to separate all the nucleons in a nucleus to infinity

(b) (i) 

Isotopes are nuclei of the same elements that have the same number of protons and different number of neutrons.

(ii) 

1784 MeV

7.57 MeV 

(c) (i)

  t half = 0.693 / λ  λ = 0.693 / (7.1 x 10⁸ x 365 x 24 x 60 x 60)

     = 3.095 x 10^-17

(ii)

  A = N λ   A = (N_A m / M) N 
  5.0 x 10³ = (6.02 x 10²³ x m / 235) 3.1 x 10^-17 

  m = 0.063 g

---

Q11(a)
1 Reflection at the surface of the metal
2 Diffraction / Scattering of X-ray inside the metal

(b) (i) 

1. ratio = 1 / exp -(0.27 x 4.0)
            = 2.94

2. ratio = [1 / exp -(0.27 x 2.5) ] x [ 1 / exp -(3.0 x 1.5)
            = 177
Note: This is ratio of incident to emerging, not the usual ratio of emerging to incident that you always practice.

(b) (ii)
 Yes, the image will have good contrast. The difference between the two ratios is large and the ratio indicates the transmission of X-ray through the specimen.

---

Q12(a)
syllabus removed

(b) (i)   4 
(b) (ii)  1011

(c)  sample value: 0 , 8 , 11 , 10 , 15 , 7 (not 8, should be rounded down) , 4 (not 5, should be rounded down) 

---

Q13(a)
advantage: 
- shorter time delay (because the orbit is lower, about a few hundred km compared to 3.6 x 10⁴ km of geostationary satellite)
- greater coverage over a long time (because Earth is rotating below as it is orbiting the Earth at the same time, see this video)

disadvantage:
- need to be tracked (because it is moving pretty fast, period is about 100 minutes)
- need a fleet of satellite (not just one) for continuous communication (again, because it is continuously moving, more satellites are aligned in such a way that at least one is always on top of a communication point)

(b)(i)

These are the frequencies linking Earth with satellite

6 GHz is the uplink frequency

and 4 GHz is the downlink frequency

(b)(ii)
It is to prevent swamping of the uplink signal by the downlink signal. This is because the uplink signal is always greatly attenuated.