NABTEB 2025 ADVANCED MECHANICAL ENGINEERING SCIENCE ANSWERS (ESSAY – TYPE A)

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MECHANICAL ENGINEERING SCIENCE ANSWERS (TYPE A)

SECTION A
INSTRUCTIONS: ANSWER ALL QUESTIONS IN THIS SECTION.

(1a)
Mechanics is the branch of physics that deals with the study of the motion of bodies, the forces acting on them, and the effects of these forces.

(1b)
(i) Statics: It is the branch of mechanics that deals with the study of bodies at rest. It focuses on analyzing forces acting on objects that are not moving and ensuring equilibrium conditions.
(ii) Dynamics: It is the branch of mechanics that deals with bodies in motion. It examines how forces affect the movement of objects, including changes in speed, direction, and acceleration.
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(2a)
Average speed is the total distance travelled by an object divided by the total time taken to cover that distance.

(2b)
Average speed = Total distance ÷ Total time. The SI unit is metre per second (m/s).
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(3a)
X1 = 50cm
X1 = 0.50m
X2 = 30.5m
X2 = 30.50m
Δx = X2 – X1
Δx= (30.50 – 0.50)m
Δx = 30.00m
Δt = 3 s
vavg = Δx/Δt
vavg = 30.00/3
vavg = 10.00m/s

(3b)
Displacement is the vector quantity that represents the change in position of an object in a specified direction.
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(4a)
Projectile motion is the motion of an object that is thrown or projected into the air and moves under the influence of gravity only, following a curved path called a trajectory.

(4b)
(i) A football kicked into the air.
(ii) Water sprayed from a hose.
(iii) A stone thrown from a hand.
(iv) An arrow shot from a bow.
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(5a)
The zeroth law of thermodynamics states that if two bodies are each in thermal equilibrium with a third body, then they are also in thermal equilibrium with each other.

(5b)
Given:
r = 18.0cm
r = 0.18m
T = 20.0°C
T = 293.15K
P = 1.05atm
R = 0.082057L·atm·mol-¹·K-¹
M(He) = 4.002602g·mol-¹
V = (4/3)πr³
V = (4/3) × π × (18.0cm)³
V = 24429.0245cm³
V = 24429.0245cm × (1L/1000cm³)
V = 24.42903L
n = PV/(RT)
n = (1.05 × 24.42903)/(0.082057 × 293.15)
n = 1.0663mol
n ≈ 1.07mol (3 s.f.)
m = n × M(He)
m = 1.0663 × 4.002602
m = 4.26808g
m ≈ 4.27g (3 s.f.)
m = 0.00427kg
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(6a)
Diffusion is the movement of particles from a region of higher concentration to a region of lower concentration until they are evenly distributed.

(6b)
Relative humidity is the percentage ratio of the actual amount of water vapour present in the air to the maximum amount of water vapour the air can hold at that temperature.
Relative humidity = (Actual vapour pressure/Saturated vapour pressure) × 100%
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(7a)
Specific heat or specific heat capacity is the amount of heat required to raise the temperature of 1 kilogram of a substance by 1 kelvin or 1°C.

(7b)
Given:
m(fe) = mass of the iron vase = 20kg
c(fe) = specific heat capacity of iron = 450J/kg·K
Ti = initial temperature = 10°C
Tf = final temperature = 90°C
ΔT = change in temperature = 80°C
Q(fe) = heat required to raise the temperature of the iron vase
Q(fe) = m(fe) × c(fe) × ΔT
Q(fe) = (mass of the iron vase) × (specific heat capacity of iron) × (change in temperature)
Q(fe) = 20 × 450 × 80
Q(fe) = 720,000J
When the Vase is filled with 20kg of water:
m(fe) = mass of the iron vase = 20kg
c(fe) = specific heat capacity of iron = 450J/kg·K
m(w) = mass of the water = 20kg
c(w) = specific heat capacity of water = 4186J/kg·K
Ti = initial temperature = 10°C
Tf = final temperature = 90°C
ΔT = change in temperature = 80°C
Q(fe) = heat required to raise the temperature of the iron vase
Q(fe) = m(fe) × c(fe) × ΔT
Q(fe) = (mass of the iron vase) × (specific heat capacity of iron) × (change in temperature)
Q(fe) = 20 × 450 × 80
Q(fe) = 720,000J
Q(w) = heat required to raise the temperature of the water
Q(w) = m(w) × c(w) × ΔT
Q(w) = (mass of the water) × (specific heat capacity of water) × (change in temperature)
Q(w) = 20 × 4186 × 80
Q(w) = 6,697,600 J
Q(total) = total heat required for iron + water
Q(total) = Q(fe) + Q(w)
Q(total) = 720,000 + 6,697,600
Q(total) = 7,417,600J
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(8a)
A closed system is a system that can exchange energy, such as heat or work, with its surroundings but cannot exchange mass with its surroundings.

(8bi)
A bomb calorimeter is a strong, sealed container used to measure the heat of combustion of a substance by burning it in a high-pressure oxygen environment and observing the resulting temperature change in the surrounding water.

(8bii)
(Draw the diagram)

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(9a)
A plane mirror is a flat, smooth reflective surface that forms an image of an object by regular reflection of light. It produces a virtual, upright, and laterally inverted image that is the same size as the object.

(9b)
Given:
do (object distance) = 20.0 cm
R (radius of curvature) = 30.0 cm
ho (object height) = 1.50 cm
f = R / 2
f = 30.0 / 2
f = 15.0 cm
1/v = 1/f – 1/do
1/v = 1/15.0 – 1/20.0
1/v = (20.0 – 15.0)/(15.0 × 20.0)
1/v = 5.0/300.0
1/v = 1/60.0
v = 60.0 cm
Image position v = 60.0cm
m = -v / do
m = -60.0 / 20.0
m = -3.0
hi = m × ho
hi = -3.0 × 1.50
hi = -4.50cm
Image height |hi| = 4.50cm (inverted)
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(10a)
Snell’s law states that when a light ray passes from one medium to another, the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant, and this ratio depends on the refractive indices of the two media.

(10b)
(Draw the diagram)

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SECTION B

(11a)
Potential energy is the energy a body possesses due to its position, condition, or state.

(11b)
(i) Gravitational potential energy
(ii) Elastic potential energy
(iii) Chemical potential energy
(iv) Electrical potential energy

(11c)
Mass (m) = 10kg
Number of steps (N) = 10
Height per step (h) = 0.2m
Total height (H) = N × h
H = 10 × 0.2
H = 2 m
Time (t) = 20s
Acceleration due to gravity (g) = 9.8m/s²
Work done (W) = m × g × H
W = 10 × 9.8 × 2
W = 196J
Power (P) = W/t
P = 196/20
P = 9.8W
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(12a)
The law of conservation of energy states that energy cannot be created or destroyed but can only be transformed from one form to another.

(12b)
Given:
Mass (m) = 10 kg
Radius of circular path (r) = 2 m
Speed (v) = 50 m/s
Centripetal acceleration (ac) = v²/r
ac = (50 × 50)/2
ac = 2500/2
ac = 1250 m/s²
Centripetal force (Fc) = m × ac
Fc = 10 × 1250
Fc = 12500N

(12c)
Angular velocity is the rate at which a body rotates or turns through an angle about a fixed point or axis.
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(13a)
(i) Expansion of substances
(ii) Change of state
(iii) Increase in temperature
(iv) Chemical changes
(v) Change in electrical resistance

(13bi)
Linear expansivity is the fractional increase in length per unit original length per unit rise in temperature.

(13bii)
Linear expansivity (α) = Increase in length/(Original length × Rise in temperature)
α = ΔL / (L × ΔT)
Where:
α = linear expansivity
ΔL = change in length
L = original length
ΔT = change in temperature

(13c)
Given:
Initial length (L₀) = 15.01 m
Final length (L) = 15.05 m
Change in length (ΔL) = L – L₀
Temperature change (Δθ) = 60°C
Linear expansivity (α) = ΔL/(L₀ × Δθ)
ΔL = 15.05 m – 15.01 m
ΔL = 0.04 m
α = ΔL/(L₀ × Δθ)
α = 0.04/(15.01 × 60)
α = 0.04/900.6
α = 4.44 × 10⁻⁵ per °C
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(14a)
(i) Railway lines: Small gaps are left between rails to allow for expansion during hot weather, preventing bending or buckling of the tracks.
(ii) Electric power lines: Cables are hung with some slack because they expand in heat and contract in cold weather, preventing snapping.
(iii) Bimetallic thermostats: They work by using two metals with different expansion rates; when heated, the strip bends and makes or breaks an electrical circuit.
(iv) Metal bridges: Expansion joints are provided to allow the bridge structure to expand and contract, preventing cracks or structural damage.

(14b)
Anomalous expansion of water is the unusual behaviour where water contracts when heated from 0°C to 4°C, reaching its maximum density at 4°C, and expands when cooled below 4°C. This is opposite to the behaviour of most substances and is important for aquatic life in cold climates.

(14c)
According to the kinetic molecular theory, conduction occurs when fast-moving (hot) particles transfer energy to slower-moving (cold) particles through direct contact. In solids, particles cannot move freely but vibrate in fixed positions; as they gain heat, they vibrate more and pass this energy to neighbouring particles, resulting in heat transfer across the material.
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(15a)
Rectilinear propagation of light is the property of light that states that light travels in straight lines through a homogeneous medium.

(15b)
(i) The incident ray, the reflected ray, and the normal at the point of incidence all lie in the same plane.
(ii) The angle of incidence is equal to the angle of reflection.

(15c)
(i) It is virtual.
(ii) It is upright (erect).
(iii) It is laterally inverted.
(iv) It is the same size as the object.
(v) It is formed at the same distance behind the mirror as the object is in front.
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