1
NSEP Topper Batch (2023)
Mechanical Properties of Fluid
1.
2.
A small sphere of mass 2.00 g is released from rest
in a large cylindrical vessel filled with oil. The
resistive force due to viscosity of oil acting on the
sphere is proportional to its velocity. Sphere
approaches a terminal speed of 5.00 cm/s. The time
it takes the sphere to reach 90.0% of its terminal
speed is approximately
[NSEP-2022]
(A) 3.22 ms
(B) 5.10 ms
(C) 10.2 ms
(D) 11.7 ms
Two plane glass testing slides each of surface area
A are stuck with each other by a small water drop
squeezed between them as an extremely thin film
of thickness d. If the surface tension of water be T
and the angle of contact is zero, then the force
required to pull apart the two glass plates will be
[NSEP-2022]
(A)
(C)
3.
4.
8TA
d
2TA
d
(B)
(D)
5.
(A) t =
(C) t =
2
. The
19 R 2
R
60a
g
17 R 2
R
60a
g
(B) t =
(D) t =
3 R 2
R
10a
g
R 2
R
4a
g
6.
If pascal (Pa), the unit of pressure, volt (V), the unit
of potential and meter (L), the unit of length are
taken as fundamental units, the dimensional formula
for permittivity 0 of free space is expressed as
[NSEP-2021]
(A) Pa–1V2L–2
(B) Pa1V–2L2
(C) Pa1V2L–2
(D) Pa–1V–2L2
7.
The flow of water in a horizontal pipe is streamline
flow. Along the pipe, at a point where the crosssectional area is 10 cm2, the velocity of water flow
is 1.00 m/s and the pressure is 2000 Pa. The
pressure of water at another point where the crosssectional area is 5 cm2 is
[NSEP-2020]
(A) 2000 Pa
(B) 1500 Pa
(C) 3500 Pa
(D) 500 Pa
8.
A home aquarium partly filled with water slides
down an inclined plane of inclination angle  with
respect to the horizontal. The surface of water in the
aquarium
[NSEP-2019]
(A) remains horizontal
(B) remains parallel to the plane of the incline
(C) forms an angle 𝛼 with the horizontal: 0 <  < 
(D) forms an angle 𝛼 with horizontal:  <  < 90
9.
A jet of water from 15 cm diameter nozzle of a fire
hose can reach the maximum height of 25 m. The
force exerted by the water jet on the hose is
[NSEP-2019]
(A) 4.24 kN
(B) 17.32 kN
(C) 2.17 kN
(D) 8.66 kN
d
A motor pump is used to deliver water at a certain
rate r from a given pipe. To obtain thrice as much
water from the same pipe in same time, the power
of the motor has to be increased to [NSEP-2022]
(A) 3 times
(B) 9 times
(C) 27 times
(D) 81 times
R
water starts dripping out through a small orifice of
cross-sectional area ‘a’ at its spherical bottom. The
time taken to get the tank completely empty (neglect
viscosity) is
[NSEP-2021]
TA
The rate of flow of a certain liquid of viscosity 
through a horizontal capillary of length l and radius
r is Q when the pressure head at the inlet is just
twice the atmospheric pressure. The rate of flow of
the same liquid through another capillary of length
2l and radius 2r when the inlet pressure head is 4
times the atmospheric pressure will be (the outlet
being open to atmosphere in each case)
[NSEP-2022]
(A) 24Q
(B) 16Q
(C) 8Q
(D) 4Q
A large hemispherical water tank of radius R is
filled with water initially upto a height h =
4TA
d
PYQ
2
10.
A 3.0 cm thick layer of oil (density ρoil= 800 kg/m3)
floats on water (density ρw = 1000 kg/m3) in a
transparent glass beaker. A solid cylinder is
observed floating vertically with
and
1
3
1
3
15.
of it in water
in the oil. Oil is gently poured into the beaker
until the cylinder floats in oil only. The fraction of
solid cylinder in oil now is
[NSEP-2019]
(A)
(C)
3
5
3
4
(B)
(D)
A solid wooden block with a uniform cross section
is floating in water (density w) with a height h1
below water. Now a flat slab of stone is placed over
the wooden block but the block still floats with a
height h2 below water. Afterwards the stone is
removed from the top and pasted at the bottom of
the wooden block. The wooden block now floats
with a height h3 under water. Therefore, the density
of the stone is
[NSEP-2016]
(A)
2
3
(C)
8
9
11.
A 20 cm long capillary tube stands vertically with
lower end just in water. Water rises up to 5 cm. If
the entire system is now kept on a freely falling
platform, the length of the water column in the
capillary tube will be
[NSEP-2019]
(A) 5 cm
(B) 10 cm
(C) zero
(D) 20 cm
12.
Two identical solid blocks A and B are made of two
different materials. Block A floats in a liquid with
half of its volume submerged. When block B is
pasted over A, the combination is found to just float
in the liquid. The ratio of the densities of the liquid,
material of A & material of B is given by
[NSEP-2017]
(A) 1 : 2 : 3
(B) 2 : 1 : 4
(C) 2 : 1 : 3
(D) 1 : 3 : 2
13.
The excess pressure inside a soap bubble is equal to
2 mm of kerosene (density 0.8 g/cc). If the diameter
of the bubble is 3.0 cm, the surface tension of the
soap solution is
[NSEP-2017]
(A) 39.2 dyne/cm
(B) 45.0 dyne/cm
(C) 51.1 dyne/cm
(D) 58.8 dyne/cm
14.
A hollow sphere of inner radius 9 cm and outer
radius 10 cm floats half submerged in a liquid of
specific gravity 0.8. The density of the material of
the sphere is
[NSEP-2017]
(A) 0.84 g/cc
(B) 1.48 g/cc
(C) 1.84 g/cc
(D) 1.24 g/cc
16.
17.
h 2 − h1
h 3 − h1
h 2 − h1
h2 − h3
w
(B)
w
(D)
h2 − 3
h 2 − h1
h3
h 2 − h1
w
w
A cup of water is placed in a car moving at a
constant acceleration a to the left. Inside the water
is a small air bubble. The figure that correctly
shows the shape of the water surface and the
direction of motion of the air bubble is
[NSEP-2016]
(A)
(B)
(C)
(D)
Water is flowing through a vertical tube with
varying cross section as shown. The rate of flow is
52.5 cm3/s. Given that speed of flow v1 = 0.35 m/s
and area of cross section A2 = 0.5 cm2. Which of
the following is/are true?
[NSEP-2016]
(A)
(B)
(C)
(D)
A1 = 1.0 cm2, v2 = 0.70 m/s
A1 = 1.5 cm2, v2 = 1.05 m/s
h = 5 cm
h = 10 cm
3
18.
19.
20.
21.
A small ball bearing is released at the top of a long
vertical column of glycerin of height 2h. The ball
bearing falls through a height h in a time t1 and then
the remaining height with terminal velocity in time
t2. Let W1 and W2 be the work done against viscous
drag over these heights. Therefore, [NSEP-2016]
(A) t1 < t2
(B) t1 > t2
(C) W1 = W2
(D) W1 < W2
A large cylindrical vessel contains water to a height
of 10 m. It is found that the thrust acting on the
curved surface is equal to that at the bottom. If
atmospheric pressure can support a water column
of 10 m, the radius of the vessel is [NSEP-2014]
(A) 10 m
(B) 15 m
(C) 5 m
(D) 25 m
23.
gradually as r = r0 e–αx where x is the distance from
the pipe and α = 0.4 m–1 is a constant. Then the ratio
of Reynolds's number for the cross sections
separated by a distance 8 m is
24.
[NSEP-2013]
(A) 24.5
(B) 28.5
(C) 2.45
(D) 2.85
The Pitot tube shown in fig. is used to measure fluid
velocity in a pipe of cross sectional area S. It was
invented by a French engineer Henri Pitot in the
early 18th century. The volume of the gas flowing
across the section of the pipe per unit time is (the
difference in the liquid columns is Δh, ρ0 and ρ are
the densities of liquid and the gas respectively)
Standing waves are generated on string loaded with
a cylindrical body. If the cylinder immersed in
water, the length of the loops changes by a factor of
2.2. The specific gravity of the material of the
cylinder is
[NSEP-2014]
(A) 1.11
(B) 2.15
(C) 2.50
(D) 1.26
A uniform meter scale is supported from its 20 cm
mark. A body suspended from 10 cm mark keeps
the scale horizontal. However, the scale gets
unbalanced if the body is completely immersed in
water. To regain the balance the body is shifted to
the 8 cm mark. Therefore, the specific gravity of the
material of the body is
[NSEP-2014]
(A) 5
(B) 6
(C) 7
(D) 4
The radius of cross section of a long pipe varies
[NSEP-2013]
(A) Q = 2 S
(C) Q = S
25.
h 0 g

h 0 g

(B) Q = S
(D) Q = S
2 h 0 g

2  h g
0
A metal body of density 8000 kg/m3 has a cavity
inside. A spring balance shows its mass to be 10 kg
in air and 7.5 kg when immersed in water. The ratio
22.
In a drip irrigation system, water flows at 0.4 m/s
through a 25 mm diameter pipe. At each of the
plants in the field water is expected to be delivered
at 0.02 m/s through a 2 mm opening. The drip
works for 2 hours a day. Then,
[NSEP-2014]
(A) the system feeds 2250 plants
(B) a plant gets about 3.2 liter of water a day
(C) the system feeds 3125 plants
(D) a plant gets about 1.8 liter of water a day
of the volume of the cavity to the volume of the
material of the body is
(A)
2
5
(C) 1
[NSEP-2013]
(B)
(D)
1
2
3
4
4
ANSWER KEY
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
(D)
(C)
(A)
(C)
(C)
(B)
(D)
(D)
(D)
(C)
(D)
(C)
(D)
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
(B)
(C)
(D)
(B, C)
(B, D)
(B)
(D)
(B)
(C)
(A)
(B)
(B)
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