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Physics specimen paper 1 TZ0 doubts

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4. yeIVVqD.jpg(Vectors not drawn to scale). Fnet = ma = mgsin θ - Ff, where positive is positive x. Ff = mg sin θ - ma

17. The main idea is to use sub topic 5.3 equation ε = I(R + r), ε is emf, R is circuit resistance, r is internal resistance. To use this equation, we have to simplify the circuit into just 1 equivalent battery source and 1 equivalent load/resistor. We already have just 1 resistor but we need to combine the 2 cells. 
Equivalent resistance of cells in parallel is 1/R = 1/R1 + 1/R2 ==> r = 1Ω.
Equivalent voltage of cells in parallel is V = V1 = V2 = ε = 1.6 V. The circuit is equivalent to a 1.6V cell of 1Ω connected to a 3Ω resistor. 

1.6V = I (3Ω + 1Ω) ==> I = 0.4A. 

18. This is just math. Slope is rise/run = -0.6/0.2 = -3 . log B = -3 log x + const ==> B = 10const x-3, B is proportional to x-3.

19. This question shows up often. By practicing more past papers you should become familiar with most of these problems. Refer to 1st equation under subtopic 6.2
A is incorrect: No gravitational forces only if infinitely far away from Earth.
B is correct: a = F/m and by same equation, acceleration is dependent upon distance from Earth, and mass of Earth, not dependent upon mass of object.
C is incorrect: equilibrium, in IB, refers to translational equilibrium, which means a balance of forces. As the astronaut and the capsule are orbiting (circular motion), the net force is non-zero. 
D is incorrect: F is dependent upon mass of object, so since astronaut and capsule have different mass, the force acted upon them is different. 

20. c = fλ (subtopic 4.1). E = hf (subtopic 7.1). Note c is speed of light, h is Plank's constant. When combined this give you λ = hc/E (also 7.1). Hence when energy decrease by a factor of 5 (from 20 to 4), wavelength increase by a factor of 5, namely from 1* 10-7 to 5 * 10-7

24. P = eσ AT4 (subtopic 8.2). Substituting T = 1.02T1 to get T4 = 1.082 ... T1 So C. You don't have a calculator but you just have to do this by hand (eg 1.02 * 1.02 = 1.0404, then truncate to 1.04 * 1.04 = 1.0816). This is why to always plug in everything carefully and never just say oh 24 = 16.
 

In summary, 4, 19 are conceptual. 18, 20, 24 are just plug in numbers correctly. 17 is both

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