# Terminal Velocity

## Trending Questions

**Q.**A spherical ball is dropped in a long column of a viscous liquid. The speed of the ball as a function of time may be best represented by the graph

- A
- B
- C
- D

**Q.**

A small sphere of radius r falls from rest in a viscous liquid. As a result, heat is produced due to viscous force. The rate of production of heat when the sphere attains its terminal velocity is proportional to

- r3
- r2
- r4
- r5

**Q.**

A balloon of mass M is descending at a constant acceleration a. When a mass m is released from the balloon, it starts rising with the same acceleration a. Assuming that its volume does not change, what is the value of m

**Q.**The terminal speed of a sphere of gold (density = 19.5 g/cm3) is 0.2 m/s in a viscous liquid (density = 1.5 g/cm3). Find the terminal speed of a sphere of silver (density =10.5 g/cm3) of the same size in the same liquid (in m/s)

**Q.**Eight equal drops of water are falling through air with a steady velocity of 5 cm/sec. If smaller drops combine to form a single large drop, then the terminal velocity (in cm/sec) of this large drop is

- 20
- 10
- 15
- 5

**Q.**A ball of mass m and radius r is released in a viscous liquid. The value of its terminal velocity is proportional to

- mr
- m
- mr
- (mr)1/2

**Q.**Two spherical rain drops with radii in the ratio 1:2 fall from a great height through the atmosphere. The ratio of their momenta after they have attained terminal velocity is:

- 1:8
- 2:1
- 1:32
- 1:2

**Q.**The ratio of the terminal velocities of two drops of same density of radii R and R/2 in air is

- 2
- 1
- 1/2
- 4

**Q.**An oil drop falls through air with a terminal velocity of 5×10−4 m/s. The radius of the drop will be:

Neglect density of air compared to that of oil. (Viscosity of air =18×10−55 N.s/m2, g=10 m/s2, density of oil =900 kg/m3

- 2.5×10−6 m
- 2×10−6 m
- 3×10−6 m
- 4×10−6 m

**Q.**Viscous drag force depends on

- Size of body
- Velocity with which it moves
- Viscosity of fluid
- All of the above

**Q.**A small spherical body of radius r is falling under gravity in a viscous medium and due to friction, the medium gets heated. When the body attains terminal velocity, then the rate of heating is proportional to:

- r1/2
- r
- r3/2
- r5

**Q.**Two rain drops reach the earth with different terminal velocities having ratio 9:4. Then the ratio of their volumes is

- 9:4
- 27:8
- 3:2
- 4:9

**Q.**Two equal drops of water are falling through air with a steady velocity v. If the drops coalesce, the new velocity will be

- 2v
- 22/3v
- √2v
- v√2

**Q.**A spherical ball of radius R is falling in a viscous fluid of viscosity η with a velocity v. The retarding viscous force acting on the spherical ball is:

- directly proportional to R but inversely proportional to v
- directly proportional to both radius R and velocity v
- inversely proportional to R but directly proportional to velocity v
- inversely proportional to both radius R and velocity v

**Q.**A spherical body falling through a viscous liquid of infinite extent ultimately attains terminal velocity, when

- Upthrust + Weight = Viscous drag
- Weight + Viscous drag = Upthrust
- Viscous drag + Upthrust = Weight
- Viscous drag + Upthrust > Weight

**Q.**

In Millikan’s oil drop experiment, what is the terminal speed of an uncharged drop of radius 2.0×10–5 m and density 1.2×103kgm–3? Take the viscosity of air at the temperature of the experiment to be 1.8×10–5 Pa s. How much is the viscous force on the drop at that speed? Neglect buoyancy of the drop due to air.

**Q.**A spherical ball of density ρ and radius 0.003 m is dropped into a tube containing a viscous fluid up to the 0 cm mark as shown in the figure. Viscosity of the fluid =1.2160 N.s m−2 and its density ρL=ρ2=1260 kg.m−3. Assume the ball reaches a terminal speed by the 10 cm mark. Find the time taken rounded off to the nearest integer (in sec) by the ball to traverse the distance between the 10 cm and 20 cm mark. Take g=10 ms−2

**Q.**When a liquid in a glass vessel is heated, its apparent expansion is 10.30 ×10−4∘C−1 . When the same liquid is heated in a metal vessel, its apparent expansion is 10.06 ×10−4∘C−1 . If the coefficient of linear expansion of glass = 9 ×10−6∘C−1 , what is the coefficient of linear expansion of metal?

- 43 × 10
^{–6}°C^{–1} - 25 × 10
^{–6}°C^{–1} - 51 × 10
^{–6}°C^{–1 } - 17 × 10
^{–6}°C^{–1}

**Q.**

A solid sphere moves at a terminal velocity of 20 ms−1 in air at a place where g=9.8 ms−2. The sphere is taken in a gravity free hall having air at the same pressure and pushed downwards at a speed of 20 ms−1. Then, identify the correct statement(s):

[Assume density of air to be very low.]

- Intial acceleration of sphere will be 9.8 ms−2 downwards.
- Initial acceleration of sphere will be 9.8 ms−2 upwards.
- The magnitude of acceleration of the sphere will decrease as time passes.
- Sphere will eventually stop.

**Q.**After terminal velocity is reached, the acceleration of a body falling through a viscous fluid is:

- Less than g
- Greater than g
- Zero
- g

**Q.**A lead shot of 1 mm diameter falls through a long column of glycerine. The variation of its velocity v with distance covered is represented by :

**Q.**

A body rolling on ice with vel. 8m/s comes to rest after traveling 4 m.Compute the co efficient of friction

**Q.**An oil drop falls through air with a terminal velocity 5×10−4 m/s. Find the radius of the drop.

Neglect the density of air as compared to that of oil. (Take viscosity of air =3.6×10−5 N-s/m2, g=10 m/s2, density of oil ρo=900 kg/m3)

- 2×10−6 m
- 2.5×10−6 m
- 4×10−6 m
- 3×10−6 m

**Q.**Find the terminal velocity of a free falling water drop of radius 0.04 mm:-

The coefficient of viscosity of air is 1.9×10−5 Ns/m2 and its density is 1.2 kg/m3. Density of water is 1000 kg/m3. Take g=10 m/s2.

- 15 cm/s
- 2.5 cm/s
- 19 cm/s
- 13 cm/s

**Q.**If the terminal speed of a sphere of gold (density = 19.5 g/cm3) is 0.2 m/s in a viscous liquid (density = 1.5 g/cm3). Find the terminal speed of a sphere of silver (density =10.5 g/cm3) of the same size in the same liquid.

- 0.4 m/s
- 0.3 m/s
- 0.25 m/s
- 0.1 m/s

**Q.**A tall cylinder is filled with viscous oil. A round pebble is dropped from the top with zero initial velocity. From the plot shown in the figure, indicate the one that represents the velocity (v) of the pebble as a function of time (t).

**Q.**Assertion: A balloon filled with hydrogen will fall with acceleration g6 of the moon.

Reason: Acceleration due to gravity is g6 on the surface of moon.

- If both assertion and reason are correct and the reason is the correct explanation of the assertion.
- If both assertion and reason are correct and the reason is not a correct explanation of the assertion.
- If the assertion is correct but reason is incorrect.
- If the assertion is incorrect but reason is correct.

**Q.**

A drop of water of radius $0.0015mm$ is falling in air. If the coefficient of viscosity of air is $2.0\times {10}^{-5}kg{m}^{-1}{s}^{-1}$, the terminal velocity of the drop will be: (The density of water $1.0\times {10}^{3}kg{m}^{-3}$ and $g=10m{s}^{-2}$)

$1.0\times {10}^{-4}m{s}^{-1}$

$2.0\times {10}^{-4}m{s}^{-1}$

$2.5\times {10}^{-4}m{s}^{-1}$

$5.0\times {10}^{-4}m{s}^{-1}$

**Q.**A solid sphere falls with a terminal velocity of 20 ms−1 in air. If it is allowed to fall in vacuum,

- Terminal velocity will be 20 ms−1.
- Terminal velocity will be less than 20 ms−1.
- Terminal velocity will be more than 20 ms−1.
- There will be no terminal velocity.

**Q.**A spherical ball of mass 4m, density σ and radius r is attached to a pulley-mass system as shown in the figure. The ball is released in a beaker with a liquid of coefficient of viscosity η and density ρ(<σ2). If the length of the liquid column in the beaker is sufficiently long, the terminal velocity attained by the ball is given by: (Assume all pulleys to be massless and strings to be massless and inextensible):

- 29r2(2σ−ρ)gη
- r2(σ−2ρ)g9η
- 29r2(σ−4ρ)gη
- 29r2(σ−3ρ)gη