Mechanical Comprehension Practice Test 1

Answer: D

Correct answer: 0 m/s². Acceleration measures how quickly velocity changes. Constant speed in a straight line means the velocity never changes, so the acceleration is zero no matter how fast the plane is going.

• A: This confuses speed with acceleration; a high speed does not mean the velocity is changing.
• B: That is the acceleration of free fall, but a plane in steady level flight is not falling.
• C: There is no change in velocity to divide by time, so no nonzero acceleration applies.
• D (correct): Its speed and direction are both constant, so its velocity is not changing and its acceleration is zero.

Answer: A

Correct answer: 500 rpm. With no slip,

• A (correct): Using D1N1 = D2N2, 1,500 times 100 / 300 = 500 rpm.
• B: Sharing a belt means the rim speeds match, not the rpm; the larger pulley turns fewer times.
• C: This divides by the diameter ratio squared (9), but speed changes by the simple diameter ratio of 3.
• D: This inverts the ratio; a larger driven pulley must turn slower, not faster.

Answer: A

Correct answer: It is the same at all three bottoms. The pressure from a still liquid is $\rho gh$, which contains no width or volume. With the same liquid and the same 2 m depth, the bottom pressure is identical in all three.

• A (correct): Liquid pressure depends only on density, g, and depth, and the depth is 2 m in every container.
• B: Slanted or flared walls do not change the pressure at a given depth.
• C: The tank holds more water, but the extra water rests on a larger floor, so pressure does not increase.
• D: Concentrating the water in a thin tube does not raise the pressure; only depth matters.

Answer: A

Correct answer: Pass a piece of cardboard near the hose. Never use skin to find a hydraulic leak, because a pinhole jet can inject oil under the skin. Use cardboard or another tool, and depressurize the system first when possible.

• A (correct): Cardboard shows the spray without putting skin in the jet's path.
• B: Raising the relief setting can exceed part ratings and makes any jet more dangerous.
• C: A fine jet of oil can pierce skin and inject fluid under it, causing a serious injury.
• D: Ordinary gloves do not stop a high-pressure jet, so this still risks an injection injury.

Answer: A

Correct answer: 450 N. Pressure is equal on both pistons, so

• A (correct): The area ratio is 36 ÷ 4 = 9, so the output force is 50 × 9 = 450 N.
• B: This multiplies by the output area alone and ignores the input area.
• C: This multiplies by the 4 square centimeter input area instead of by the area ratio of 9.
• D: This flips the area ratio, as if the larger piston reduced the force.

Answer: D

Correct answer: 0.05 m. At rest the spring force balances the weight, so

The weight is

• A: This treats the 3 kg mass as a 3 N force instead of converting it to weight with mg.
• B: This halves the correct stretch, as if the spring carried only half the weight.
• C: This is a decimal slip, dividing 30 N by 60 instead of 600.
• D (correct): The weight is 3 times 10, or 30 N, and 30 divided by 600 gives 0.05 m.

Answer: B

Correct answer: 90 s. Rearrange

to get

J ÷ 500 W = 90 s.

• A: This divides power by work, inverting the relationship t = W/P.
• B (correct): Time equals work divided by power: 45,000 ÷ 500 = 90 s.
• C: This is ten times too long, a place-value slip in the division.
• D: This is ten times too short, a place-value slip in the division.

Answer: A

Correct answer: 180 W. Work against gravity: W = mgh =

• A (correct): Work is 60 × 10 × 12 = 7,200 J, and 7,200 ÷ 40 = 180 W.
• B: This uses mass instead of weight, leaving out g.
• C: This is the work in joules; it still has to be divided by the 40 s.
• D: This is ten times too large, a place-value slip in the division.

Answer: C

Correct answer: It accelerates north, with a net force of 30 N. Treat each direction separately. East-west:

North-south:

N toward the north. Since one sum is not zero, the ring accelerates north.

• A: Both the horizontal and the vertical sums must be zero; the vertical sum is not.
• B: This adds all four magnitudes, ignoring that opposite forces subtract.
• C (correct): Horizontal forces cancel (50 − 50 = 0), but vertically 70 − 40 = 30 N is left over toward the north.
• D: The larger vertical pull is the 70 N northward one, so the leftover force points north.

Answer: D

The 48-tooth driver moves three output circumferences per turn, so

This response follows the specified gear geometry and the assumptions in the question.

• A: This is the reciprocal reduction calculation, which would suit a small driver and large output.
• B: Unequal tooth counts on a direct mesh do not produce one-to-one speeds.
• C: 144 rpm does not follow from the tooth ratio 48/16 = 3; the output must be 90 × 3 = 270 rpm.
• D (correct): The 48-tooth driver moves three output circumferences per turn, so 90(48/16) = 270 rpm.

Answer: B

Correct answer: 440. Put both lengths in meters: 5 mm = 0.005 m.

• A: Dividing the radius by the lead leaves out the 2 pi needed for the full circle.
• B (correct): IMA is 2 pi times 0.35 m divided by 0.005 m, which is about 440.
• C: Using 0.35 m as a radius and then doubling again treats it as a diameter in the formula.
• D: Using pi times the radius counts only half of the handle's circular path.

Answer: C

Correct answer: 1.5 m from the pivot. Counterclockwise moment:

N·m. Clockwise moments must also total 600 N·m:

• A: This ignores the 300 N child already on the right, making the 200 N child balance all 600 N·m alone.
• B: This subtracts the weights first (400 minus 300) instead of subtracting the moments.
• C (correct): The left moment is 600 N·m; the 300 N child supplies 300 N·m, so the 200 N child must supply 300 N·m at 1.5 m.
• D: This adds the 300 N·m on the right to the left side's moment instead of subtracting it.

Answer: B

Correct answer: The water, about 31 times as much. Bolt:

Water:

840,000/27,000 ≈ 31, so the cooler but much larger, high-specific-heat water holds far more energy.

• A: This compares only the temperatures, 300/40, ignoring mass and specific heat.
• B (correct): The water releases 840,000 J and the bolt releases 27,000 J; 840,000/27,000 is about 31.
• C: Temperature alone does not set stored thermal energy; mass and specific heat matter too.
• D: This compares only the specific heats, 4,200/450, and leaves out the masses and temperature drops.

Answer: A

Correct answer: 100 N, pointing down the ramp. Gravity's pull along the ramp is

N downhill. The 300 N push up the ramp exceeds it by 100 N, so static friction supplies 100 N down the ramp. The limit is

so the crate stays at rest.

• A (correct): The push exceeds gravity's 200 N downhill pull by 100 N, so the crate tends to move uphill and friction holds it back.
• B: This ignores gravity's downhill component, which already balances part of the push.
• C: This is the static limit, which is reached only when the crate is about to slip.
• D: Friction opposes the tendency to slip, and here the net tendency is uphill, not downhill.

Answer: B

Correct answer: 250 rpm and 55.2 N·m. Output speed is set only by the tooth ratio:

Efficiency lowers the torque, not the speed:

N·m.

• A: This applies the efficiency to the speed, but teeth cannot slip, so speed stays exactly as the ratio sets it.
• B (correct): Speed follows the tooth ratio exactly, 1,000 / 4 = 250 rpm, and torque is 0.92 times 4 times 15 = 55.2 N·m.
• C: These are the ideal values; the 92 percent efficiency must reduce the torque.
• D: This reduces both speed and torque, counting the friction loss twice.