GCAT Mechanical Reasoning Concepts 2 — Questions and Answers
Question 1: A hydraulic press has an input piston with area 2 cm² and an output piston with area 20 cm². If you apply 50 N to the input, what force does the output produce?
- 100 N
- 250 N
- 500 N (Correct answer)
- 1000 N
Correct answer: 500 N
Pascal's law: output force = input force × (output area / input area) = 50 × (20/2) = 500 N.
Question 2: Two gears mesh together. Gear A has 10 teeth and Gear B has 40 teeth. If Gear A rotates at 200 RPM, how fast does Gear B rotate?
- 800 RPM
- 100 RPM
- 50 RPM (Correct answer)
- 40 RPM
Correct answer: 50 RPM
Gear speed ratio is inverse to tooth ratio: Gear B = 200 × (10/40) = 50 RPM.
Question 3: A block rests on a ramp inclined at 30°. Compared to lifting it straight up, the ramp requires approximately how much force (ignoring friction)?
- The same force
- Half the force (Correct answer)
- Twice the force
- One-quarter the force
Correct answer: Half the force
An inclined plane reduces required force by sin(angle); sin(30°) = 0.5, so half the force is needed.
Question 4: Water flows through a pipe that narrows from a 4-inch diameter to a 2-inch diameter. What happens to the water's velocity in the narrow section?
- It halves
- It doubles
- It quadruples (Correct answer)
- It stays the same
Correct answer: It quadruples
By the continuity equation, velocity × cross-sectional area is constant; area drops by factor 4, so velocity quadruples.
Question 5: A spring with a spring constant of 200 N/m is compressed by 0.05 m. How much elastic potential energy is stored?
- 0.10 J
- 0.25 J (Correct answer)
- 5.0 J
- 10.0 J
Correct answer: 0.25 J
Elastic PE = ½kx² = ½ × 200 × (0.05)² = 0.25 J.
Question 6: A wrench 30 cm long applies 60 N·m of torque to a bolt. What force is being applied to the end of the wrench?
- 2 N
- 200 N (Correct answer)
- 0.5 N
- 1800 N
Correct answer: 200 N
Torque = force × lever arm; force = torque / arm = 60 / 0.30 = 200 N.
Question 7: A pulley system uses a single movable pulley. What is the mechanical advantage?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
A single movable pulley provides a mechanical advantage of 2 because two rope segments support the load.
GCAT Mechanical Reasoning Concepts 2
A hydraulic press has an input piston with area 2 cm² and an output piston with area 20 cm².
If you apply 50 N to the input, what force does the output produce?