Mechanical Aptitude Ultimate Questions and Answers 2 — Questions and Answers

Question 1: A gear train has a 20-tooth input gear, a 40-tooth idler gear, and a 60-tooth output gear. What is the overall gear ratio?

1:2
1:3 (Correct answer)
2:3
1:6

Correct answer: 1:3

The idler gear does not affect the gear ratio. The overall ratio is output teeth / input teeth = 60/20 = 3:1 (or input:output = 1:3). The 40-tooth idler only changes the rotation direction of the output.

In a gear train, idler gears transmit motion between non-adjacent gears without affecting the overall speed ratio. The idler receives a ratio from the input (40/20 = 2:1 reduction) and transmits it to the output (60/40 = 1.5:1 reduction), but the net ratio is simply output teeth / input teeth = 60/20 = 3:1. Mathematically: (40/20) × (60/40) = 60/20. The 40 cancels because it appears in both numerator and denominator. The idler's only function is to change the output direction (even number of meshes = same direction as input; odd number = opposite) or to span a distance between the input and output shafts. This principle applies regardless of the idler's size.

Question 2: A hydraulic press has an input piston area of 5 cm² and an output piston area of 100 cm². If the input force is 200N, what force is produced at the output?

1,000N
2,000N
4,000N (Correct answer)
10,000N

Correct answer: 4,000N

By Pascal's principle, pressure is equal: P = F₁/A₁ = F₂/A₂. Therefore F₂ = F₁ × (A₂/A₁) = 200N × (100/5) = 200 × 20 = 4,000N.

Pascal's principle states that pressure is transmitted equally throughout a confined fluid. The input pressure is P = F₁/A₁ = 200N / 5cm² = 40 N/cm². This same pressure acts on the output piston: F₂ = P × A₂ = 40 N/cm² × 100 cm² = 4,000N. The force multiplication factor is A₂/A₁ = 100/5 = 20. However, conservation of energy means the input piston must travel 20 times farther than the output piston moves. If the output needs to move 1 cm, the input must be pumped through 20 cm of travel. This trade-off between force and distance is fundamental to all hydraulic systems, from car jacks to industrial presses capable of hundreds of tons of force.

Question 3: A 500 kg load is lifted 4 meters using a pulley system with 80% efficiency. How much work input is required?

15,680 J
19,600 J
24,500 J (Correct answer)
39,200 J

Correct answer: 24,500 J

Useful work output = mgh = 500 × 9.8 × 4 = 19,600 J. With 80% efficiency: Work input = Output / Efficiency = 19,600 / 0.80 = 24,500 J.

This problem combines work calculation with efficiency. Step 1: Calculate the useful work output (lifting the load against gravity): W_out = mgh = 500 kg × 9.8 m/s² × 4 m = 19,600 J. Step 2: Account for system inefficiency. Efficiency (η) = useful output / total input, so input = output / η = 19,600 J / 0.80 = 24,500 J. The extra 4,900 J (24,500 - 19,600) represents energy lost to friction in the pulleys, rope stiffness, and other real-world losses. In practice, pulley systems lose about 2-5% per sheave (pulley wheel), so an 80% efficient system might have 4-5 sheaves. This calculation is essential for selecting motors and energy sources for lifting equipment.

Question 4: Two springs with spring constants k₁ = 200 N/m and k₂ = 300 N/m are connected in parallel. What is the combined spring constant?

120 N/m
250 N/m
500 N/m (Correct answer)
600 N/m

Correct answer: 500 N/m

For springs in parallel, the combined spring constant is the sum: k_total = k₁ + k₂ = 200 + 300 = 500 N/m. Parallel springs share the load and are stiffer together.

When springs are connected in parallel (both attached between the same two points, side by side), they share the applied force but undergo the same displacement. Each spring provides its own restoring force, so the total force for a given displacement is the sum: F_total = k₁x + k₂x = (k₁ + k₂)x. Therefore k_parallel = k₁ + k₂ = 200 + 300 = 500 N/m. This is the opposite of springs in series, where k_series = (k₁ × k₂)/(k₁ + k₂) = (200 × 300)/(200 + 300) = 120 N/m. The parallel combination is always stiffer (higher k) than either individual spring, while the series combination is always more compliant (lower k) than the weakest spring. Vehicle suspension systems use parallel springs for increased load capacity.

Question 5: An engine produces 150 kW of power. How much work does it perform in 30 seconds?

5,000 J
4,500 J
4,500,000 J (Correct answer)
450,000 J

Correct answer: 4,500,000 J

Power = Work / Time, so Work = Power × Time = 150,000 W × 30 s = 4,500,000 J (or 4.5 MJ). Remember that 1 kW = 1,000 W and 1 W = 1 J/s.

Power is defined as the rate at which work is done or energy is transferred: P = W/t, or equivalently W = P × t. Converting units: 150 kW = 150,000 W = 150,000 J/s. Over 30 seconds: W = 150,000 J/s × 30 s = 4,500,000 J = 4.5 MJ (megajoules). For context, this is equivalent to lifting about 115 metric tons one meter against gravity, or roughly the energy in 125 grams of gasoline (at ~35% engine efficiency). This relationship between power, work, and time is fundamental to engineering: it determines fuel consumption rates, electrical energy bills (kWh = power in kW × time in hours), and the sizing of motors and engines for specific tasks.

Question 6: A beam supported at both ends carries a 600N point load at its center. What is the reaction force at each support?

600N each
300N each (Correct answer)
200N each
150N each

Correct answer: 300N each

For a simply supported beam with a centered point load, each support carries half the load due to symmetry. Reaction at each end = 600N / 2 = 300N. The upward forces (300N + 300N) equal the downward force (600N), satisfying equilibrium.

For a beam in static equilibrium, two conditions must be satisfied: the sum of all vertical forces equals zero (ΣF = 0), and the sum of all moments about any point equals zero (ΣM = 0). For a center load, symmetry immediately tells us each reaction is equal. Formally: taking moments about the left support — R_right × L = 600 × (L/2), so R_right = 300N. By vertical equilibrium: R_left + R_right = 600N, so R_left = 300N. If the load were not centered (say, at 1/3 of the span from the left), the reactions would be unequal: R_right = 200N and R_left = 400N (the support closer to the load carries more). This principle of static equilibrium is fundamental to structural engineering and is applied to every beam, bridge, and building design.

Mechanical Aptitude Ultimate Questions and Answers 2

A gear train has a 20-tooth input gear, a 40-tooth idler gear, and a 60-tooth output gear.
What is the overall gear ratio?