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PHYSICS OBJ
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PART I: ANSWER FIVE(5) QUESTIONS ONLY
(1)
R = (U²Sin2θ)/g
Where:
-U is the initial velocity (dimension: LT⁻¹, where L is length and T is time)
-θ is the angle (dimensionless)
-g is the acceleration due to gravity (dimension: LT⁻²)
Now, let’s determine the dimension of R:
R = (U²Sin2θ)/g
R = U²/g
= ((LT⁻¹)² / (LT⁻²)
= (L²T⁻²) / (LT⁻²)
= L
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(2)
(i) Gas Laser:
It used in cutting and welding materials.
(ii) Chemical Laser:
It is often used in military applications such as missile defense systems.
(iii) Dye Laser:
It is used in spectroscopy for studying chemical structures and reactions.
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(3)
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(4)
Given:
v = 5.8 km/s = 5800 m/s
T = 20.2 hours = 72720 s
R = 6400km = 6.4 × 10⁶m
Using the formula:
v = 2πr / T
r = vT / 2π
r = (5800 × 72720 s) / (2 × 3.14)
r = 67.16 × 10⁶ m
h = r – R
= (67.16 × 10⁶) – (6.4 × 10⁶)
= 60.76 × 10⁶m
= 60,760,000 m
= 60,760 km
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(5)
Given:
Initial extension = 0.04 m when F = 6 N
spring constant (k):
k = F /e
= 6 N / 0.04 m
= 150 N/m
New extension when F = 8 N:
e = F / k
= 8 N/150 N/m
= 0.0533 m
New length = Natural length + New extension
= 5 m + 0.0533 m
= 5.0533 m
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(6)
(i) Laser light consists of a single wavelength, while white light contains a mixture of many wavelengths
(ii) The waves in laser light are in phase, while the waves in white light are out of phase.
(iii) Laser beams travel in a narrow, focused path while white light diverges and illuminates a broad area
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(7)
(i) The retentivity of a magnetic material is its ability to retain a residual magnetic flux density (Br) after the external magnetizing field (H) is removed, following saturation.
(ii) A material with high magnetic susceptibility is iron
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PART II: ANSWER THREE (3) QUESTIONS ONLY
(8ai)
A semiconductor is said to be doped when impurities are intentionally added to it to alter its electrical properties.
(8aii)
I. Intrinsic semiconductor:
An intrinsic semiconductor is a pure semiconductor material without any impurities, where the number of electrons and holes is equal.
II. Extrinsic semiconductor:
An extrinsic semiconductor is a semiconductor material that has been doped with impurities to alter its electrical properties, resulting in an unequal number of electrons and holes (p-type or n-type).
(8b)
(8c)
Given:
Wavelength (λ) = 3.0 × 10⁻⁷ m
Kinetic energy (KE) = 1.5 × 10⁻¹⁹ J
c = 3.0 × 10⁸ m/s
mₑ = 9.1 × 10⁻³¹ kg
h = 6.6 × 10⁻³⁴ Js
(i) Maximum velocity of the photoelectron
KE = (1/2)mv²
1.5 × 10⁻¹⁹ J = (1/2) × 9.1 × 10⁻³¹ kg × v²
v² = 2 × 1.5 × 10⁻¹⁹ J / (9.1 × 10⁻³¹ kg)
v² = 3.3 × 10¹¹
v = √(3.3 × 10¹¹)
v ≈ 5.74 × 10⁵ m/s
(ii) Work function of the metal
E = hc / λ
= (6.6 × 10⁻³⁴ Js × 3.0 × 10⁸ m/s) / (3.0 × 10⁻⁷ m)
= 6.6 × 10⁻¹⁹ J
Work function (φ) = E – KE
= 6.6 × 10⁻¹⁹ J – 1.5 × 10⁻¹⁹ J
= 5.1 × 10⁻¹⁹ J
(8d)
Stopping potential is the minimum potential difference required to stop the most energetic electrons emitted from a material from reaching the collector, effectively reducing the photocurrent to zero.
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(9a)
Deformation refers to the change in shape or size of a material due to an external force, while elasticity is the ability of a material to return to its original shape after the force is removed.
(9bi)
(9bii)
Slope = ∆F/∆e
Point 1: (Extension = 10.0 cm, Force = 2.0 N)
Point 2: (Extension = 30.0 cm, Force = 6.0 N)
S = (6.0-2.0)/(30.0-10.0)
S = 4.0/20.0
S = 0.2N/cm
(9biii)
The slope represents the spring constant
k, indicating the stiffness of the spring.
(9c)
Given:
Mass (m) = 40 g = 0.04 kg
Elastic constant (k) = 350 N/m
Extension (x) = 4 cm = 0.04 m
Elastic potential energy stored in the rubber(E) = (1/2)kx²
= (1/2) × 35 × (0.04)²
(1/2) × 35 × 0.0016
= 0.28 J
This energy is converted to kinetic energy of the stone:
K = (1/2)mv² = E
(1/2)mv² = 0.28 J
(1/2) × 0.04 × v² = 0.28
v² = (2 × 0.28)/0.04
v² = 14
v = √14
v = 3.74 m/s
(9d)
(i) Bulk modulus
Bulk modulus is a measure of a material’s resistance to compression under uniform pressure.
(ii) Energy gained by the wire
Given:
Mass (m) = 2.5g = 0.0025kg
Extension (x) = 2cm = 0.02m
g = 10m/s²
Force (F) = mg = 0.0025 × 10 = 0.025N
Energy gained (E) = (1/2)Fx
= (1/2) × 0.025 × 0.02
= 2.5 × 10⁻⁴ J
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(10a)
(i) First overtone;
The first overtone is the second harmonic of a vibrating system, having a frequency twice that of the fundamental frequency.
(ii) End correction;
End correction accounts for the fact that the antinode of a standing wave in a pipe doesn’t exactly coincide with the physical end.
(10b)
Given:
Length (L) = 40 cm = 0.4 m
End correction (e) = 3.2 cm = 0.032 m
Velocity of sound (v) = 330 m/s
Effective length = L + e = 0.4 + 0.032 = 0.432m
Wave length (λ)= 4Leff
λ = 4×0.432
= 1.728m
Frequency (f) = v/λ=
= 330/1.728
= 191Hz
(10ci)
Given: n = 8
n = 360° / β – 1
360° / β = n + 1
360° / β = 8 + 1
360° / β = 9
β = 360° / 9
β = 40°
(10cii)
(i) Mirage involves refraction and total internal reflection in air, while total internal reflection occurs at a medium boundary.
(ii) Mirage produces an inverted image, while total internal reflection produces a mirror-like reflection.
(10ciii)
Given: f₀ = 3 cm, fe = 6 cm, L = 20 cm
v₀ = L – fe = 20 – 6 = 14 cm
1/f₀ = 1/v₀ – 1/u₀
1/3 = 1/14 – 1/u₀
1/u₀ = 1/14 – 1/3
1/u₀ = (3 – 14) / 42
1/u₀ = -11 / 42
u₀ = -42 / 11
u₀ = -3.82 cm
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(11a)
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(12)
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