JEE Physics Mechanical Properties Of Fluids MCQs Set 06

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Chapter-wise Objective Questions: Mechanical Properties Of Fluids

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Multiple Choice Questions

Question 1:
Assertion (A): The size of a hydrogen balloon increases as it rises in air.
Reason (R): The material of the balloon can be easily stretched.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. The outside pressure falls with height, so the gas expands
2. The balloon stretches easily, which is true but is not the reason for the expansion

Teacher's Note:
1. Decide whether each statement is true, then whether R explains A.

Question 2: A hydraulic press is based upon:
(a) Archimedes' principle
(b) Bernoulli's theorem
(c) Pascal's law
(d) Reynolds number
Show Answer & Explanation

Answer: (c) Pascal's law

Explanation:
1. The hydraulic press transmits pressure equally through the liquid

Teacher's Note:
1. Apply the standard formula and check the units.

Question 3: A wooden block is taken to the bottom of a lake of water and then released. It rises with a:
(a) constant acceleration
(b) decreasing acceleration
(c) constant velocity
(d) decreasing velocity
Show Answer & Explanation

Answer: (a) constant acceleration

Explanation:
1. Buoyant force and weight are both constant while the block is fully immersed, so the net force and acceleration are constant (ignoring drag)

Teacher's Note:
1. Apply the standard formula and check the units.

Question 4: Two water pipes P and Q of diameters \( 2\times10^{-2} \) m and \( 4\times10^{-2} \) m are joined in series with the main supply line of water. The velocity of water in pipe P is:
(a) 4 times that in Q
(b) 2 times that in Q
(c) 1/2 times that in Q
(d) 1/4 times that in Q
Show Answer & Explanation

Answer: (a) 4 times that in Q

Explanation:
1. A1 v1 = A2 v2, so v is inversely proportional to d^2
2. vP/vQ = (4/2)^2 = 4

Teacher's Note:
1. Apply the standard formula and check the units.

Question 5: The cylindrical tube of a spray pump has radius R, one end of which has n fine holes, each of radius r. If the speed of flow of the liquid in the tube is v, the speed of ejection through a hole is:
(a) \( \frac vn\frac Rr \)
(b) \( \frac{v}{n}\left(\frac Rr\right)^{1/2} \)
(c) \( \frac{v^2}{n^2}\frac Rr \)
(d) \( \frac vn\left(\frac Rr\right)^2 \)
Show Answer & Explanation

Answer: (d) \( \frac vn\left(\frac Rr\right)^2 \)

Explanation:
1. Continuity: pi R^2 v = n pi r^2 u
2. u = (v/n)(R/r)^2

Teacher's Note:
1. Apply the standard formula and check the units.

Question 6:
Assertion (A): A needle placed carefully on the surface of water may float, whereas a ball of the same material will always sink.
Reason (R): The buoyancy of an object depends both on the material and on the shape of the object.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (c) A is true, but R is false.

Explanation:
1. The needle is held by surface tension, so A is true
2. Buoyancy depends only on displaced volume, not on the material, so R is false

Teacher's Note:
1. Decide whether each statement is true, then whether R explains A.

Question 7: Water from a tap emerges vertically downwards with an initial speed of 1.0 m/s. The cross-sectional area of the tap is \( 10^{-4} \) m2. The flow is steady and the pressure is constant throughout the stream. The cross-sectional area of the stream 0.15 m below the tap is (g = 10 m/s2):
(a) \( 5.0\times10^{-4} \) m2
(b) \( 1.0\times10^{-4} \) m2
(c) \( 5.0\times10^{-5} \) m2
(d) \( 2.0\times10^{-5} \) m2
Show Answer & Explanation

Answer: (c) \( 5.0\times10^{-5} \) m2

Explanation:
1. v^2 = u^2 + 2gh = 1 + 3 = 4, so v = 2 m/s
2. A v = A0 u gives A = 1e-4 x 1/2 = 5e-5 m2

Teacher's Note:
1. Apply the standard formula and check the units.

Question 8: A tank of height 5 m is full of water. There is a hole of cross-sectional area 1 cm2 in its bottom. The initial volume of water that will come out of this hole per second is (g = 10 m/s2):
(a) \( 10^{-3} \) m3/s
(b) \( 10^{-4} \) m3/s
(c) 10 m3/s
(d) \( 10^{-2} \) m3/s
Show Answer & Explanation

Answer: (a) \( 10^{-3} \) m3/s

Explanation:
1. Speed = sqrt(2 g h) = 10 m/s
2. Rate = 1e-4 x 10 = 1e-3 m3/s

Teacher's Note:
1. Apply the standard formula and check the units.

Question 9: The pressure of water in a water pipe when the tap is opened and closed is \( 3\times10^5 \) N/m2 and \( 3.5\times10^5 \) N/m2 respectively. With the tap open, the velocity of water flowing is:
(a) 10 m/s
(b) 5 m/s
(c) 20 m/s
(d) 15 m/s
Show Answer & Explanation

Answer: (a) 10 m/s

Explanation:
1. Pressure drop = 0.5e5 Pa = (1/2) rho v^2
2. v^2 = 2 x 0.5e5/1000 = 100, so v = 10 m/s

Teacher's Note:
1. Apply the standard formula and check the units.

Question 10: The flow speeds of air on the lower and upper surfaces of the wing of an aeroplane are v and \( \sqrt2 v \) respectively. The density of air is rho and the surface area of the wing is A. The dynamic lift on the wing is:
(a) \( \rho v^2A \)
(b) \( \sqrt2\rho v^2A \)
(c) \( \tfrac12\rho v^2A \)
(d) \( 2\rho v^2A \)
Show Answer & Explanation

Answer: (c) \( \tfrac12\rho v^2A \)

Explanation:
1. Pressure difference = (1/2) rho (2v^2 - v^2) = (1/2) rho v^2
2. Lift = (1/2) rho v^2 A

Teacher's Note:
1. Apply the standard formula and check the units.

Question 11:
Assertion (A): The velocity of horizontal flow of an ideal liquid is smaller where the pressure is large, and vice versa.
Reason (R): According to Bernoulli's theorem for streamline flow of an ideal liquid, the total energy per unit mass remains constant.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. At constant height, P + (1/2) rho v^2 is constant
2. So high pressure goes with low speed, and R explains A

Teacher's Note:
1. Decide whether each statement is true, then whether R explains A.

Question 12: An incompressible fluid flows steadily through a cylindrical pipe which has radius 2R at point A and radius R at point B farther along the flow direction. If the velocity at A is v, its velocity at B is:
(a) 2v
(b) v
(c) v/2
(d) 4v
Show Answer & Explanation

Answer: (d) 4v

Explanation:
1. A1 v1 = A2 v2 gives pi(2R)^2 v = pi R^2 vB, so vB = 4v

Teacher's Note:
1. Apply the standard formula and check the units.

Question 13: Water flows through a non-uniform tube. The ratio of the radii at the entry and exit ends is 3 : 2. The ratio of the velocities at entry and exit is:
(a) 4 : 9
(b) 9 : 4
(c) 8 : 27
(d) 1 : 1
Show Answer & Explanation

Answer: (a) 4 : 9

Explanation:
1. v is proportional to 1/r^2, so v1/v2 = (2/3)^2 = 4/9

Teacher's Note:
1. Apply the standard formula and check the units.

Question 14: An aeroplane of mass \( 3\times10^4 \) kg and total wing area 120 m2 is in level flight. The difference in pressure between the upper and lower surfaces of its wings in kilopascals is (g = 10 m/s2):
(a) 2.5
(b) 5.0
(c) 10.0
(d) 12.5
Show Answer & Explanation

Answer: (a) 2.5

Explanation:
1. Lift balances weight: Delta P x A = m g
2. Delta P = 3e4 x 10/120 = 2500 Pa = 2.5 kPa

Teacher's Note:
1. Apply the standard formula and check the units.

Question 15: A scent sprayer is based on:
(a) Charles' law
(b) Archimedes' principle
(c) Boyle's law
(d) Bernoulli's theorem
Show Answer & Explanation

Answer: (d) Bernoulli's theorem

Explanation:
1. Fast air over the nozzle lowers pressure and sucks the liquid up (Bernoulli)

Teacher's Note:
1. Apply the standard formula and check the units.

Question 16:
Assertion (A): The shape of an automobile is designed so that its front resembles the streamline pattern of the fluid through which it moves.
Reason (R): The shape of the automobile is streamlined in order to reduce the resistance offered by the fluid.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. A streamlined body avoids eddies, which reduces drag
2. So R explains A

Teacher's Note:
1. Decide whether each statement is true, then whether R explains A.

Question 17: Bernoulli's equation for steady non-viscous incompressible flow expresses the:
(a) conservation of angular momentum
(b) conservation of density
(c) conservation of momentum
(d) conservation of mechanical energy
Show Answer & Explanation

Answer: (d) conservation of mechanical energy

Explanation:
1. It is the work-energy theorem for a flowing fluid

Teacher's Note:
1. Apply the standard formula and check the units.

Question 18: Bernoulli's theorem can be seen in the application of:
(a) dynamic lift of an aeroplane
(b) hydraulic press
(c) speed boat
(d) none of these
Show Answer & Explanation

Answer: (a) dynamic lift of an aeroplane

Explanation:
1. Faster air above the wing gives lower pressure and so lift
2. A hydraulic press uses Pascal's law

Teacher's Note:
1. Apply the standard formula and check the units.

Question 19: The velocity of water flowing in a non-uniform tube is 20 cm/s at a point where the radius is 0.2 cm. The velocity at another point where the radius is 0.1 cm is:
(a) 80 cm/s
(b) 40 cm/s
(c) 20 cm/s
(d) 5 cm/s
Show Answer & Explanation

Answer: (a) 80 cm/s

Explanation:
1. v is proportional to 1/r^2
2. The radius halves, so the velocity becomes 4 x 20 = 80 cm/s

Teacher's Note:
1. Apply the standard formula and check the units.

Question 20: A small drop of water falls from rest through a large height h in air. The final velocity is:
(a) almost independent of h
(b) proportional to sqrt(h)
(c) proportional to h
(d) inversely proportional to h
Show Answer & Explanation

Answer: (a) almost independent of h

Explanation:
1. The drop reaches a terminal velocity, which does not depend on the height of fall

Teacher's Note:
1. Apply the standard formula and check the units.

Question 21:
Assertion (A): A parachute descends slowly whereas a stone dropped from the same height falls rapidly.
Reason (R): The viscous force of air on the parachute is larger than that on a falling stone.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (a) Both A and R are true, and R is the correct explanation of A.

Explanation:
1. The large area of the parachute gives a large drag
2. The terminal speed is therefore small

Teacher's Note:
1. Decide whether each statement is true, then whether R explains A.

Question 22: Two drops of equal radius fall through air with a steady velocity of 5 cm/s. If the two drops coalesce, the terminal velocity will be:
(a) \( 4^{1/3}\times5 \) cm/s
(b) \( 4^{1/3} \) cm/s
(c) \( 5^{1/3}\times4 \) cm/s
(d) \( 4^{2/3}\times5 \) cm/s
Show Answer & Explanation

Answer: (a) \( 4^{1/3}\times5 \) cm/s

Explanation:
1. The radius of the new drop is R = 2^(1/3) r
2. Terminal velocity is proportional to r^2, so v = 2^(2/3) x 5 = 4^(1/3) x 5 cm/s

Teacher's Note:
1. Apply the standard formula and check the units.

Question 23: The terminal speed of a sphere of gold (density 19.5 g/cm3) is 0.2 m/s in a viscous liquid of density 1.5 kg/m3. The terminal speed of a sphere of silver (density 10.5 g/cm3) of the same size in the same liquid is:
(a) 0.4 m/s
(b) 0.133 m/s
(c) 0.1 m/s
(d) 0.2 m/s
Show Answer & Explanation

Answer: (c) 0.1 m/s

Explanation:
1. v is proportional to (rho - sigma)
2. Gold gives 18 and silver 9, so the speed is half, 0.1 m/s

Teacher's Note:
1. Apply the standard formula and check the units.

Question 24: The speed of a 2 cm radius ball in a viscous liquid is 20 cm/s. The speed of a 1 cm radius ball in the same liquid is:
(a) 5 cm/s
(b) 10 cm/s
(c) 40 cm/s
(d) 80 cm/s
Show Answer & Explanation

Answer: (a) 5 cm/s

Explanation:
1. Terminal speed is proportional to r^2
2. Halving the radius gives one-fourth, so 5 cm/s

Teacher's Note:
1. Apply the standard formula and check the units.

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Multiple Choice Questions (MCQs) for JEE Physics Mechanical Properties Of Fluids

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