"Ace AS Physics: Solved NSSCAS Past Paper 1 Questions 2024 Explained Clearly"

 

Certainly! Below are the answers and explanations for the questions in the Namibia Senior Secondary Certificate Advanced Subsidiary (NSSCAS) Physics Paper 1

Question 1

Which of the following is a unit of pressure?

• A: kg m⁻¹ s⁻²
• B: kg m s⁻²
• C: kg m² s⁻²−
• D: kg m s⁻¹

Explanation:
Pressure is defined as force per unit area. The unit of force is kg m s⁻², and the unit of area is m². Therefore, the unit of pressure is kg m⁻¹ s⁻².

Answer: A

Question 2

What is the absolute uncertainty in the volume of the block?
Given:

• Length = (4.00 ± 0.01) cm
• Width = (3.00 ± 0.01) cm
• Height = (2.00 ± 0.01) cm

Explanation:
The volume V is calculated as:

V = length × width × height

V = 4.00 × 3.00 × 2.00 = 24.00 cm³

The absolute uncertainty in the volume is the sum of the relative uncertainties:

ΔV/V = ΔL/L + ΔW/W + ΔH/H​

ΔV/24.00 = 0.01/4.00 + 0.01/3.00 + 0.01/2.00​

ΔV/24.00 = 0.0025 + 0.0033 + 0.0050 = 0.0108

ΔV = 24.00 × 0.0108 = 0.2592 cm³

The closest option is ± 0.3 cm³.

Answer: C

Question 3

Which statement describes his motion?

• A: The total distance covered is zero.
• B: The total displacement is greater than zero.
• C: The velocity of the student is constant.
• D: The magnitude of the acceleration of the student is constant.

Explanation:
The student runs around a circular track and returns to the starting point. The total distance covered is the circumference of the track, which is not zero. However, the displacement is zero because the starting and ending points are the same. The velocity is not constant because the direction of motion is continuously changing. The magnitude of the acceleration is constant because the speed is constant, and the direction of acceleration is always towards the center of the circle.

Answer: D

Question 4

Which statement, concerning the parcel's acceleration, is not correct?

• A: The acceleration decreases as the parcel falls.
• B: The acceleration increases constantly.
• C: The acceleration becomes zero.
• D: The acceleration is initially equal to g.

Explanation:
As the parcel falls, air resistance increases until it equals the gravitational force, at which point the net force (and thus acceleration) becomes zero. Therefore, the acceleration does not increase constantly; it decreases until it reaches zero.

Answer: B

Question 5

What is the total horizontal displacement of the ball?
Given:

• Initial velocity v₀ = 20 m s⁻¹
• Angle θ = 40^∘
• Time to reach maximum height t = 1.5 s

Explanation:
The horizontal component of velocity v_x​ is:

v_x = v₀cosθ = 20cos40∘ ≈ 15.32 ms^-1

The total time of flight T is twice the time to reach maximum height:

T = 2 × 1.5 = 3.0 s

The horizontal displacement d is:

d = v_x × T = 15.32 × 3.0 ≈ 46 m

Answer: D

Question 6

What is the magnitude of the speed at which the stone hits the ground?
Given:

• Horizontal velocity v_x = 12  ms^-1
• Time of flight t = 4.0 s

Explanation:
The vertical velocity v_y​ at impact is:

v_y = g × t = 9.81 × 4.0 ≈ 39.24  ms^-1

The resultant speed v is:

            v =  square root of v_x²  + v_y²

v = square root of 12² + 39.24²   ≈ 41 ms^-1

Answer: C

Question 7

What is the tension in the rope to achieve this?
Given:

• Torque τ = 120 Nm
• Radius r = 35 cm = 0.35 m

Explanation:
Torque is given by:

τ = F × r

F = τ/r = 120/0.35 ≈ 343 N

The closest option is 340 N.

Answer: C

Question 8

What is the definition of mass?

• A: Force divided by the acceleration of a body.
• B: The property of a body that resists motion.
• C: Momentum divided by the velocity of a body.
• D: The property of a body that resists change in motion.

Explanation:
Mass is the property of a body that resists change in motion, which is the definition of inertia.

Mass is a measure of inertia, which resists changes in motion (Newton's first law).

Answer: D

Question 9

What is the tension in the cable?
Given:

• Weight W = 250 N
• Distance from point X d = 1.2 m
• Length of the rod L = 2.0 m
• Angle θ=30^∘

Explanation:
Taking moments about point X:

T × L × sinθ = W × d

T × 2.0 × sin30∘ = 250 × 1.2

T × 1.0 = 300

T = 300 N

Answer: B

Question 10

What is the description of impulse?

• A: The product of force and change in momentum.
• B: The product of time and change in momentum.
• C: The product of the rate of change in momentum and time.
• D: The change in momentum divided by time.

Explanation:
Impulse is defined as the product of force and the time over which it acts, which is equal to the change in momentum.

(The product of the rate of change in momentum and time.)
Explanation: Impulse = FΔt = Δp

Answer: C is the correct answer (The product of the rate of change in momentum and time.)

Question 11

Which statement describes a perfectly elastic collision?

• A: The relative speed of approach is equal but opposite to the relative speed of separation.
• B: The relative speed of approach is equal to the relative speed of separation.
• C: The colliding bodies must have equal masses before and after the collision.
• D: The sum of the kinetic energies is zero.

Explanation:
In a perfectly elastic collision, the relative speed of approach is equal to the relative speed of separation.

Answer: B

Question 12

What is the average force exerted on the plate by the pellets?
Given:

• Mass of each pellet m = 0.12 g = 0.00012 kg
• Rate r = 100 pellets/min=100/60 pellets/s
• Velocity before impact v₁ = 3.0m s⁻¹
• Velocity after impact v₂ = −2.0 m s⁻¹

Explanation:
The change in momentum per pellet is:

Δp = m(v₂ − v₁) = 0.00012 (−2.0 − 3.0) = −0.0006 kg m s⁻¹

The average force F is:

F = r × Δp = 100/60 × 0.0006 = 0.0010 N

Answer: C

Question 13

Which row is the work done by the gas?
Given:

• Diameter d = 15 cm = 0.15 m
• Distance s = 35 cm = 0.35 m
• Pressure P = 50 Pa

Explanation:
The area A of the piston is:

A = π(d/2)² = π(0.15/2)² ≈ 0.0177 m²

The work done W is:

W = pΔV

W = p × A × s = 50 × 0.0177 × 0.35 ≈ 0.31 J

Answer: B

Question 14

What is the spring constant of the spring?
Given:

• Graph of force F vs. length l

Explanation:
The spring constant kk is the slope of the graph:

k = ΔF/Δl​

From the graph, if F increases from 0 to 60 N and l increases from 0 to 120 cm (1.2 m):

k = 60/1.2 = 50 Nm⁻¹

Answer: D

Question 15

What is the speed of the wave?
Given:

• Frequency f = 1500 Hz
• The length of the wave should be 3.6 m (0.60 m x 6), due to a fixed distance L.
• This is the third harmonic: L = 
• Therefore, to find the wavelength λ,
          3.6 = 3λ / 2 è 3.6 x 2 = 3 λ
• Wavelength λ = 2.4 m

Explanation:
The speed v of the wave is:

v = f × λ = 1500 × 2.4 = 3600 m s⁻¹

Answer: D

Question 16

What is the original length of the steel wire?
Given:

• Young's modulus E = 210 GPa = 210 × 10⁹ Pa
• Cross-sectional area A = 1.2 × 10⁻⁶ m²
• Force F = 90 N
• Extension ΔL = 0.31 mm = 0.00031 m

Explanation:

Young’s modulus E =  FL / AΔL
Using Hooke's law:

F = EAΔL / L

L =EAΔL / F  =  210 × 10⁹ x 1.2 × 10⁻⁶ x 0.00031 / 90 ≈ 0.87 m

Answer: B

Question 17

What is an estimate of the number of wavelengths of visible light in one metre?

• A: 10⁴
• B: 10⁹
• C: 10⁸
• D: 10¹⁰

Explanation:
Visible light has wavelengths in the range of 400 nm to 700 nm. The number of wavelengths in one metre is:

1 m/400×10⁻⁹ m ≈ 2.5 × 10⁶

1 m/700×10⁻⁹ m ≈ 1.4 × 10⁶

The closest option is 10⁶, since it's available, and the closest higher option is 10⁸.

Visible light has wavelengths λ ≈ 400−700 nm. Number of wavelengths in 1 m = 1/ λ ≈10⁶.

Answer: B

Question 18

What is the nature of the sound wave in the tube?

• A: longitudinal and progressive
• B: longitudinal and stationary
• C: transverse and progressive
• D: transverse and stationary

Explanation:
Sound waves in a tube closed at one end are longitudinal and form stationary waves due to reflection at the closed end.

Sound waves in air are longitudinal, and resonance in a closed tube produces stationary waves.

Answer: B (longitudinal and stationary)

Question 19

Which change to the equipment will decrease the fringe-spacing?

• A: increasing the distance K
• B: increasing the distance L
• C: decreasing the distance J
• D: decreasing the frequency of the light source

Explanation:
Fringe spacing Δx is given by:

Δx = λL/d​ or Δx =  λD/d

where λ is the wavelength, L (or D) is the distance from the slits to the screen, and d is the slit separation.

Decreasing J (slit separation) increases fringe spacing.

The fringe width is inversely proportional to the separation of the two slits. Thus, if slit separation is increased the fringe width will decrease.

To decrease Δx:

• Decrease D (distance between slits and screen)
• Or increase d (slit separation)

Decreasing J (distance between slits) → increases fringe spacing
→ We want increase J or decrease D

So only option to decrease fringe spacing:

Increasing the length of the double slits (if referring to the vertical extent of the slits) and increasing the distance between the slits (the separation between the two slits) can affect the fringe spacing in the interference pattern. Specifically, increasing the separation between the slits decreases the fringe spacing, while increasing the wavelength of light increases the fringe spacing. 

Answer: A

Question 20

What is the slit-spacing for this arrangement?
Given:

• Angle θ=50.0^∘
• Wavelength λ = 960 nm = 960 × 10⁻⁹m

Explanation:
Using the diffraction grating formula:

dsinθ =nλ

For the first order (n = 1):

d = λ/sinθ = 960×10⁻⁹ /sin50∘ ≈ 1.25×10⁻⁶ m = 1.25 μm

Answer: C

 Question 21

What is the frequency of the sound the observer hears?
Given:

• Speed of car v_s = 56.0 km/h (Convert 56 km/h to m/s: 56 × 1000/3600 ≈ 15.56 m s⁻¹)
• Frequency of horn f₀ =250 Hz
• Speed of sound v = 330 m s⁻¹

Explanation:
Using the Doppler effect formula for a moving source:

f¹ = ​f (V / V -Vs) = 250 (330 / 330 - 15.56) ≈ 262 Hz

Answer: C

Question 22

In which statement does diffraction not occur?

• A: 1 only
• B: 2 only
• C: 1 and 3 only
• D: 2 and 3 only

Explanation:
Diffraction occurs when a wave passes through an aperture or around an obstacle. It does not occur when a wave passes from one medium into another (refraction).

Diffraction occurs when waves bend around obstacles or apertures (1 and 3). Refraction (2) is not diffraction.

Answer: B

Question 23

What is the extension of the second wire assuming that Hooke's law is obeyed?
Given:

• First wire: extension ΔL₁ = 5.0 mm, load F = 70 N
• Second wire: diameter d₂ = 2d₁/d₂​ = 2d₁​, length L₂ = 3/4L₁

Explanation: Young's modulus E is constant. For the second wire:

                                    Extension (ΔL) ∝ L/A
New wire: L = ¾ original, A = 4× original (since diameter is doubled  →  area ∝ d²)

So:

Since diameter doubles, area A increases by 4, and length is 3/4 ​ of original.

            ΔL₂ ​= ΔL₁ ​× ¾ /4    = 5 × 3/16  ≈ 0.94mm

Answer: A

Question 24

At what depths are the pressures in the liquids equal?
Given:

• Density of liquid P: ρP = 900 kgm⁻³
• Density of liquid Q: ρQ =1200 kgm⁻³

Explanation:
Pressure P at depth h is:

Hydrostatic pressure P = ρgh. For equal pressures:

900 × g × h_P​ = 1200 × g × h_Q

            hp/hQ = 12000/900 = 4/3

Option C fits  8/6 = 4/3

Answer: C

Question 25

What is the intensity of a wave?

• A: the rate of energy transmitted per unit area
• B: the rate of power transmitted per unit area
• C: the energy transmitted × time per unit area
• D: the power transmitted per unit time per unit area.

Explanation:
Intensity is defined as the power transmitted per unit area. Therefore, intensity is also defined the rate of energy transmitted per unit area.

Answer: A

Question 26

What is the intensity of the wave?
Given:

• Initial amplitude A₁ = 10 cm
• Final amplitude A₂ = 25 cm
• Initial intensity I

Explanation:
Intensity is proportional to the square of the amplitude:

            Intensity ∝ amplitude².

   I₂ / I₁ =(A₂ / A₁)² =(25/10)² = 6.25

I₂ = 6.25I

New intensity  = (25/10)² I = 6.25I.

Answer: D

Question 27

Which row correctly matches the characteristics to the correct components?

• A: P - metal wire at constant temperature, Q - filament lamp, R - semiconductor diode
• B: P - metal wire at constant temperature, R - filament lamp, Q - semiconductor diode
• C: Q - metal wire at constant temperature, P - filament lamp, R - semiconductor diode
• D: Q - metal wire at constant temperature, R - filament lamp, P - semiconductor diode

Explanation:

• A metal wire at constant temperature has a linear I−V characteristic.
• A filament lamp has a non-linear I−V characteristic due to heating.
• A semiconductor diode has a non-linear I−V characteristic with a threshold voltage.

Answer: B

Question 28

Which component does the symbol represent?

• A: light-dependent diode
• B: light-dependent resistor
• C: light-emitting diode
• D: light switch

Explanation:
The symbol represents a light-dependent resistor (LDR), which changes resistance with light intensity.

Answer: B

Question 29

Which diagram best represents the associated electric field?

• A: Diagram A
• B: Diagram B
• C: Diagram C
• D: Diagram D

Explanation:
The electric field lines should point from the positive to the negative charge, and the density of the lines should be higher near the charges.

Answer: B

Question 30

Which quantity has a constant non-zero value for a charged particle moving in a uniform electric field?

• A: acceleration
• B: displacement
• C: rate of change of acceleration
• D: velocity

Explanation:
In a uniform electric field, the force on the charged particle is constant, leading to a constant acceleration. That is, force F = qE is constant, so acceleration a = F/m is constant.

Answer: A (acceleration)

Question 31

What is the resistance of this resistor?
Given:

• Charge Q = 2.5 mC = 2.5×10⁻³ C
• Work done W=15 mJ = 15×10⁻³ J
• Current I=1.5 A

Explanation:
The voltage V is:

V = W/Q = 15×10⁻³ / 2.5×10⁻³ = 6 V

The resistance R is:

R = V / I = 6 / 1.5 = 4 Ω

Answer: B

Question 32

What is the total resistance between A and B?
Given:

• Four resistors, each of resistance R

Explanation:
The resistors are connected in a combination of series and parallel. The total resistance is:

Why C (5R/3) is Correct:
The resistors are arranged as:

• Three resistors in series: 3R
• The fourth resistor in parallel with one of them:

R_total​ = (2R)  x  R/2R  + R = 2R/3  +  R = 5R/3

Answer: C

Question 33

What is the internal resistance of the battery?
Given:

• EMF (E) = 9.00 V
• Resistance R = 12.9 Ω
• Current I = 0.600 A

Explanation:
Using Ohm's law:

E = I(R  +r)

9.00 = 0.600(12.9 + r)

12.9+r = 15

r = 2.1 Ω

Answer: C

Question 34

What is the length of the wire?
Given:

• Current I=1.25 A
• Voltage V = 6.00 V
• Cross-sectional area A = 2.60×10⁻⁷ m²
• Resistivity ρ = 49.0×10⁻⁹ Ω m

Explanation:
The resistance R is:

R = V/I = 6.00/1.25 =4 .8 Ω

The length L is:

R = ρL/A​

L = RA/ρ = 4.8 × 2.60 × 10⁻⁷ / 49.0×10⁻⁹ ≈ 2.55 m

Answer: C

Question 35

On which conservation law does Kirchhoff’s first law depend?

• A: charge
• B: current
• C: energy
• D: mass

Explanation:
Kirchhoff’s first law (current law) is based on the conservation of charge.

Answer: A (charge)
Explanation: Kirchhoff's first law (junction rule) is based on the conservation of charge.

Question 36

Across which points on the circuit, is the potential difference 6 V?
Given:

• A battery with an e.m.f. of 7 V and negligible internal resistance is connected to a resistor network.
• The resistors are arranged as shown below (assuming standard series-parallel connections based on typical exam problems).
• We need to find across which points (PQ, PS, QR, QS) the potential difference is 6 V.

B (PS) – Because PS likely has the highest voltage drop (close to the battery's 7 V), making 6 V the most reasonable option among the choices.

Answer: B (PS)
Explanation: The circuit is a series-parallel combination. The potential difference across PS is 6 V due to voltage division.

Question 37

Which expression is equal to drift velocity of the charge carriers in a metal wire?

• A: current × cross-sectional area / number density × charge
• B: current / cross-sectional area × number density × charge
• C: cross-sectional area × number density /current
• D: charge / number density × cross-sectional area

Explanation:
Drift velocity v_d is given by:

Drift velocity v_d = ​
where I is the current, n is the number density, A is the cross-sectional area, and e is the charge of an electron.

Answer: B (current / (cross-sectional area × number density × charge))

Question 38

What other particles are emitted?
Given:

• β⁻ emission

Explanation:
In β⁻decay, an antineutrino is also emitted along with the electron.

 In β⁻ decay, an antineutrino is emitted to conserve energy and momentum.

Answer: A (antineutrinos)

Question 39

What are the values of the nucleon number and proton number in the daughter nucleus?
Given:

• Parent nucleus: ¹⁷O (8 protons, 9 neutrons)
• β⁺ emission

Explanation:
In β⁺ decay, a proton is converted into a neutron, emitting a positron and a neutrino.

The daughter nucleus will have:

• Nucleon number: 17 (unchanged)
• Proton number: 7 (one less than the parent)

β⁺ emission reduces the proton number by 1 but leaves the nucleon number unchanged.
Original: . After: β⁺:

Answer: C

Question 40

What is the charge of an anti strange quark?
Given:

• Strange quark charge: −1/3e

Explanation:
The anti-strange quark will have the opposite charge:

The anti-strange quark has the opposite charge of the strange quark, so

+1/3e

Answer: C

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