Mechanical Comprehension Practice Test 4

Answer: D

Rigidly fixed gears co-rotate with the shared shaft even when their pitch diameters and tooth counts differ. This response follows the specified gear geometry and the assumptions in the question.

• A: At equal angular speed, tangential speed increases with radius, so differently sized gears need not match.
• B: Torque can be introduced or extracted at different positions; shaft balance cannot be inferred from gear size alone.
• C: Gears of different diameters and tooth counts can be fixed on the same shaft.
• D (correct): Rigidly fixed gears co-rotate with the shared shaft even when their pitch diameters and tooth counts differ.

Answer: A

Correct answer: Screw. A screw is an inclined plane wrapped around a cylinder. Its spiral thread acts as a ramp, so a long circular hand motion moves the load a short way along the axis.

• A (correct): A screw thread is a sloped path wrapped around a cylinder, so turning it moves the load along the axis.
• B: A wedge is a slope that moves into a gap; it is not wound around a shaft.
• C: A ramp is a fixed, flat sloped surface that the load travels up, with no spiral.
• D: A pulley is a grooved wheel with a rope, not a sloped surface at all.

Answer: B

Correct answer: 0.04 m³. Since 1 m³ = 1,000 L, divide by 1,000:

• A: This uses 1 L = 0.0001 m³, which is ten times too small.
• B (correct): One liter is 0.001 m³, so 40 L is 40 × 0.001 = 0.04 m³.
• C: This uses 1 L = 0.1 m³, which is a hundred times too large.
• D: This uses 1 L = 0.01 m³, which is ten times too large.

Answer: D

Correct answer: Velocity. A vector needs both a magnitude and a direction. Velocity, force, acceleration and displacement are vectors, while mass, time, temperature, distance and speed are scalars.

• A: A temperature like 20 degrees has no direction, so it is a scalar.
• B: Mass has only a size, such as 5 kg, so it is a scalar.
• C: An amount of time such as 30 seconds needs no direction, so it is a scalar.
• D (correct): Velocity has both a size and a direction, such as 15 m/s north, so it is a vector.

Answer: B

Correct answer: 0.6 s. Since

making $k$ four times larger divides the period by

• A: This multiplies by 4, reversing the effect of stiffness and ignoring the square root.
• B (correct): Period goes as the square root of m/k, so 4 times the stiffness halves the period to 0.6 s.
• C: This divides the period by 4, forgetting that the period depends on the square root of k.
• D: This doubles the period, but a stiffer spring makes the motion faster, not slower.

Answer: C

Correct answer: 4 m/s². Subtract friction from the push to get the net force, then divide by mass.

• A: This divides the friction force alone by the mass.
• B: This adds friction to the push instead of subtracting it.
• C (correct): The net force is 140 minus 60, or 80 N, and 80 N divided by 20 kg is 4 m/s².
• D: This ignores friction and divides the full push by the mass.

Answer: A

Correct answer: 25 N. Treat the plank's weight as acting at its center, 1.2 m from the short end, which is

m beyond the sawhorse on the long side. Its moment is

N·m. The can sits 0.80 m from the sawhorse on the other side, so it must weigh

• A (correct): The plank's center is 1.2 m from each end, 0.40 m past the sawhorse; its 20 N·m moment divided by the can's 0.80 m arm is 25 N.
• B: This simply copies the plank's weight; the plank's weight acts only 0.40 m from the pivot, a shorter arm than the can's 0.80 m.
• C: This ignores the plank's own weight, which acts at its center and tips the plank toward the longer side.
• D: This flips the arms, multiplying by 0.80 and dividing by 0.40.

Answer: C

Correct answer: 70 N. With no vertical acceleration, the upward normal force must equal the total downward force:

• A: This subtracts the push, which would be right only if the worker were lifting up.
• B: This counts only the worker's push and leaves out the box's weight.
• C (correct): The floor must balance both the 50 N weight and the 20 N downward push: 50 + 20 = 70 N.
• D: The normal force equals the weight only when no other vertical forces act.

Answer: A

Correct answer: 1.2 m. Balance the moments about the pivot.

The heavier rider sits closer to the center, as expected.

• A (correct): Setting moments equal: 300 times 1.8 is 540 N·m, and 540 divided by 450 is 1.2 m.
• B: This flips the force ratio; the heavier person must sit closer to the pivot, not farther.
• C: Sitting at the same distance would only balance if the two weights were equal.
• D: This is just 300 divided by 450 and leaves out the child's 1.8 m distance.

Answer: B

Correct answer: About 1,885 W. Convert rpm to rad/s, then multiply by torque.

• A: This doubles the correct value, an extra factor of 2 in the conversion.
• B (correct): Converting 600 rpm to about 62.8 rad/s and multiplying by 30 N·m gives about 1,885 W.
• C: This multiplies torque by rpm directly; P = τω needs angular speed in rad/s.
• D: This uses 10 revolutions per second without the factor 2π radians per revolution.

Answer: B

Correct answer: 10 s. When objects approach head-on, the closing speed is the sum of their speeds:

• A: This uses only the faster cart's speed, giving about 17 s.
• B (correct): Moving head-on, the gap closes at 7 + 5 = 12 m/s, and 120 m divided by 12 m/s is 10 s.
• C: This uses the difference of the speeds, which applies only when one object chases another.
• D: This uses only the slower cart's speed and ignores the other cart's motion.

Answer: C

Correct answer: 400,000 J.

At 30 m/s:

At 10 m/s:

The brakes absorb

• A: This uses the speed change of 20 m/s in the energy formula; energy depends on each speed squared, not on the difference.
• B: This is the full starting kinetic energy, as if the car stopped completely.
• C (correct): The kinetic energy drops from 450,000 J to 50,000 J, a loss of 400,000 J that becomes heat.
• D: This leaves out the one-half in the kinetic energy formula.

Answer: B

Correct answer: 0.72 J. Parallel stiffness is

N/m, so both springs compress

The stiffer spring holds three times the energy of the softer one (0.72 J versus 0.24 J).

• A: This is the total energy in both springs, not the share held by the 900 N/m spring.
• B (correct): Both springs compress 48/1200 = 0.04 m, so the 900 N/m spring stores one-half of 900 times 0.04 squared, which is 0.72 J.
• C: This is the energy in the 300 N/m spring; in parallel the stiffer spring stores more, not less.
• D: This multiplies the spring's final force by its compression without the factor of one-half.

Answer: C

Correct answer: 1,885 W. Belt speed:

Power = (400 N - 160 N) x 7.85 m/s, about 1,885 W.

• A: This leaves pi out of the belt speed, using D x N / 60 instead of the circumference.
• B: This uses only the tight-side tension and ignores the slack side pulling back.
• C (correct): Belt speed is pi x 0.12 x 1,250 / 60, about 7.85 m/s, and (400 - 160) x 7.85 is about 1,885 W.
• D: This adds the two tensions, but the turning force is their difference.

Answer: B

Correct answer: 12 s. Volume needed:

cubic centimeters. Flow: 9,000 cubic centimeters per minute divided by 60 is 150 cubic centimeters per second.

• A: This divides 1,800 cubic centimeters by 15 instead of 150, a decimal slip in the flow rate.
• B (correct): The stroke needs 1,800 cubic centimeters, and 9 L per minute is 150 cubic centimeters per second, so it takes 12 s.
• C: 0.2 minute was turned into seconds by multiplying by 100 instead of 60.
• D: This divides 1.8 L by 9 L correctly but reads the result as seconds; the flow rate is per minute, so the answer is 0.2 minute.