Free Terminal Velocity MCQs with Answers

1. A body falling through a fluid reaches terminal velocity when

• A. the drag force becomes zero
• B. the upward drag and upthrust together balance the weight, so the net force is zero
• C. the body stops moving completely
• D. gravity stops acting on the body

Explanation: Drag increases with speed, so the body accelerates until the retarding forces grow to match its weight, after which the acceleration is zero and the speed stays constant. The body is still moving, and gravity still acts; what has vanished is the resultant force, not any individual one. This is why a raindrop reaches the ground at a survivable speed rather than accelerating for its whole fall.

2. The terminal velocity of a small sphere falling through a viscous liquid is proportional to

• A. the radius of the sphere
• B. the square of the radius of the sphere
• C. the inverse of the radius
• D. the viscosity of the liquid

Explanation: Equating the weight less upthrust to the Stokes drag gives a terminal velocity proportional to r squared and inversely proportional to viscosity, so a sphere of twice the radius falls four times as fast. This is why fine dust hangs in the air for hours while a pebble drops at once. Raising the viscosity lowers the terminal velocity rather than raising it.

3. Two spheres of the same size but different densities fall through the same viscous liquid. The denser one has

• A. the same terminal velocity
• B. a lower terminal velocity
• C. a higher terminal velocity
• D. no terminal velocity

Explanation: Terminal velocity depends on the difference between the density of the sphere and that of the fluid, so a denser sphere needs a larger drag force to balance its greater weight and must therefore fall faster to generate it. Radius and viscosity being equal, density is the only variable left. If the sphere were less dense than the liquid it would rise instead.

4. A skydiver opens a parachute. The terminal velocity

• A. falls, because the larger area increases the drag at a given speed
• B. rises, because the parachute adds weight
• C. is unchanged
• D. becomes zero immediately

Explanation: Opening the canopy multiplies the effective area and therefore the drag, so the forces balance again at a much lower speed and the diver decelerates towards the new terminal velocity. The weight is essentially unchanged, so it is the drag side of the balance that has altered. The speed never reaches zero, which is why a landing roll is still needed.

5. When an object attains terminal velocity, its acceleration is:

• A. 9.8 m/s2 upward
• B. Zero
• C. 1 m/s2
• D. 9.8 m/s2 downward

Explanation: At terminal velocity the upward drag and upthrust exactly balance the weight, so the resultant force is zero and by Newton's second law the acceleration is zero, even though the body continues to fall at a steady speed. What has vanished is the resultant force, not any individual one. This is why a raindrop reaches the ground at a survivable speed.