Solved Example: Fluid Mechanics | Physics for JEE Main & Advanced PDF Download

 Page 1


JEE Solved Example on Fluid Mechanics 
JEE Mains 
Q1:  The area of cross-section of the wider tube shown in figure is ?????? ????
?? . If a mass of ???? ???? is 
placed on the massless piston, the difference in heights ?? in the level of water in the two tubes is: 
 
(A) ???? ???? 
(B) ?? ???? 
(C) ???? ???? 
(D) ?? ???? 
Ans:  (C) Pressure due to difference in heights will be balanced by pressure due to 12 kg block 
 ? ???? h =
120
800 × 10
-4
10
4
 h =
120
800
× 10
4
 h =
12
80
=
3
20
 m = 15 cm
 
 
 
Q2:  Two cubes of size ?? . ?? ?? side, one of relative density 0.60 and another of relative density =
?? . ???? are connected by weightless wire and placed in a large tank of water. Under equilibrium the 
lighter cube will project above the water surface to a height of: 
(A) ???? ???? 
(B) ???? ???? 
(C) ???? ???? 
(D) Zero 
Ans: (B) 
Page 2


JEE Solved Example on Fluid Mechanics 
JEE Mains 
Q1:  The area of cross-section of the wider tube shown in figure is ?????? ????
?? . If a mass of ???? ???? is 
placed on the massless piston, the difference in heights ?? in the level of water in the two tubes is: 
 
(A) ???? ???? 
(B) ?? ???? 
(C) ???? ???? 
(D) ?? ???? 
Ans:  (C) Pressure due to difference in heights will be balanced by pressure due to 12 kg block 
 ? ???? h =
120
800 × 10
-4
10
4
 h =
120
800
× 10
4
 h =
12
80
=
3
20
 m = 15 cm
 
 
 
Q2:  Two cubes of size ?? . ?? ?? side, one of relative density 0.60 and another of relative density =
?? . ???? are connected by weightless wire and placed in a large tank of water. Under equilibrium the 
lighter cube will project above the water surface to a height of: 
(A) ???? ???? 
(B) ???? ???? 
(C) ???? ???? 
(D) Zero 
Ans: (B) 
 
Downward force on the cubes = ( ?? 1
+ ?? 2
) g 
 = ?? 1
???? + ?? 2
????
 ( 1750)× 10
 
Upward force on the cubes = ?? ( ?? 1
+ ?? ) ?? 
= 1000( h + 1)× 10 
Since cubes are in equilibrium 
So 17500 = 10000 ( h + 1) 
1.75 - 1 = h
 ? h = 0.75 m
 
 
 
Q3:  A cuboidal piece of wood has dimensions ?? , ?? and c. Its relative density is ?? . It is floating in a 
large body of water such that side a is vertical. It is pushed down a bit and released. The time 
period of SHM executed by it is: 
(A) ?? ?? v
??????
?? 
(B) ?? ?? v
?? ????
 
(C) ?? ?? v
????
????
 
(D) ?? ?? v
????
?? 
Ans: D 
Page 3


JEE Solved Example on Fluid Mechanics 
JEE Mains 
Q1:  The area of cross-section of the wider tube shown in figure is ?????? ????
?? . If a mass of ???? ???? is 
placed on the massless piston, the difference in heights ?? in the level of water in the two tubes is: 
 
(A) ???? ???? 
(B) ?? ???? 
(C) ???? ???? 
(D) ?? ???? 
Ans:  (C) Pressure due to difference in heights will be balanced by pressure due to 12 kg block 
 ? ???? h =
120
800 × 10
-4
10
4
 h =
120
800
× 10
4
 h =
12
80
=
3
20
 m = 15 cm
 
 
 
Q2:  Two cubes of size ?? . ?? ?? side, one of relative density 0.60 and another of relative density =
?? . ???? are connected by weightless wire and placed in a large tank of water. Under equilibrium the 
lighter cube will project above the water surface to a height of: 
(A) ???? ???? 
(B) ???? ???? 
(C) ???? ???? 
(D) Zero 
Ans: (B) 
 
Downward force on the cubes = ( ?? 1
+ ?? 2
) g 
 = ?? 1
???? + ?? 2
????
 ( 1750)× 10
 
Upward force on the cubes = ?? ( ?? 1
+ ?? ) ?? 
= 1000( h + 1)× 10 
Since cubes are in equilibrium 
So 17500 = 10000 ( h + 1) 
1.75 - 1 = h
 ? h = 0.75 m
 
 
 
Q3:  A cuboidal piece of wood has dimensions ?? , ?? and c. Its relative density is ?? . It is floating in a 
large body of water such that side a is vertical. It is pushed down a bit and released. The time 
period of SHM executed by it is: 
(A) ?? ?? v
??????
?? 
(B) ?? ?? v
?? ????
 
(C) ?? ?? v
????
????
 
(D) ?? ?? v
????
?? 
Ans: D 
 
Initially in equilibrium 
When pushed down by y distance, an extra upward force will act on the cube 
?? ( ?????? ) ?? = ???????????? [?? = ???????????????????????? of the cube] 
?? =
????
?? ?? ? ?? =
?? ????
?? ? ?? 2
=
?? ????
? ?? = v
?? ????
? ?? =
2?? ?? = 2?? v
????
?? 
 
Q4:  The frequency of a sonometer wire is ?? , but when the weights producing the tensions are 
completely immersed in water the frequency becomes ?? /?? and on immersing the weights in a 
certain liquid the frequency becomes ?? /?? . The specific gravity of the liquid is: 
(A) 
?? ?? 
(B) 
????
?? 
(C) 
????
????
 
(D) 
????
????
 
Ans: (D) ?? ? v ?? , ?? = tension in the wire in water frequency becomes f/2 ? Tension becomes 1/4 of 
the initial in liquid frequency becomes ?? /3 
 
? Tension become 1/9 of the initial 
For water ?? ? ?? =
3????
4
 
for liquid d?? Vg =
8
9
mg 
? ?? =
8
27
× 4 =
32
27
 
 
 
Page 4


JEE Solved Example on Fluid Mechanics 
JEE Mains 
Q1:  The area of cross-section of the wider tube shown in figure is ?????? ????
?? . If a mass of ???? ???? is 
placed on the massless piston, the difference in heights ?? in the level of water in the two tubes is: 
 
(A) ???? ???? 
(B) ?? ???? 
(C) ???? ???? 
(D) ?? ???? 
Ans:  (C) Pressure due to difference in heights will be balanced by pressure due to 12 kg block 
 ? ???? h =
120
800 × 10
-4
10
4
 h =
120
800
× 10
4
 h =
12
80
=
3
20
 m = 15 cm
 
 
 
Q2:  Two cubes of size ?? . ?? ?? side, one of relative density 0.60 and another of relative density =
?? . ???? are connected by weightless wire and placed in a large tank of water. Under equilibrium the 
lighter cube will project above the water surface to a height of: 
(A) ???? ???? 
(B) ???? ???? 
(C) ???? ???? 
(D) Zero 
Ans: (B) 
 
Downward force on the cubes = ( ?? 1
+ ?? 2
) g 
 = ?? 1
???? + ?? 2
????
 ( 1750)× 10
 
Upward force on the cubes = ?? ( ?? 1
+ ?? ) ?? 
= 1000( h + 1)× 10 
Since cubes are in equilibrium 
So 17500 = 10000 ( h + 1) 
1.75 - 1 = h
 ? h = 0.75 m
 
 
 
Q3:  A cuboidal piece of wood has dimensions ?? , ?? and c. Its relative density is ?? . It is floating in a 
large body of water such that side a is vertical. It is pushed down a bit and released. The time 
period of SHM executed by it is: 
(A) ?? ?? v
??????
?? 
(B) ?? ?? v
?? ????
 
(C) ?? ?? v
????
????
 
(D) ?? ?? v
????
?? 
Ans: D 
 
Initially in equilibrium 
When pushed down by y distance, an extra upward force will act on the cube 
?? ( ?????? ) ?? = ???????????? [?? = ???????????????????????? of the cube] 
?? =
????
?? ?? ? ?? =
?? ????
?? ? ?? 2
=
?? ????
? ?? = v
?? ????
? ?? =
2?? ?? = 2?? v
????
?? 
 
Q4:  The frequency of a sonometer wire is ?? , but when the weights producing the tensions are 
completely immersed in water the frequency becomes ?? /?? and on immersing the weights in a 
certain liquid the frequency becomes ?? /?? . The specific gravity of the liquid is: 
(A) 
?? ?? 
(B) 
????
?? 
(C) 
????
????
 
(D) 
????
????
 
Ans: (D) ?? ? v ?? , ?? = tension in the wire in water frequency becomes f/2 ? Tension becomes 1/4 of 
the initial in liquid frequency becomes ?? /3 
 
? Tension become 1/9 of the initial 
For water ?? ? ?? =
3????
4
 
for liquid d?? Vg =
8
9
mg 
? ?? =
8
27
× 4 =
32
27
 
 
 
Q5:  A small ball of relative density 0.8 falls into water from a height of ?? ?? . The depth to which 
the ball will sink is (neglect viscous forces): 
(A) ?? ?? 
(B) ?? ?? 
(C) ?? ?? 
(D) ?? ?? 
Ans: (A) By work energy theorem 
?? water 
+ ?? gravity 
= ????? = 0
?? water 
= ( ?????? ) h
?? gravity 
= -( 0.8?? hg) ( h + 2)
 ? ?????? h - 0.8?????? ( h + 2) = 0
h - 0.8( h + 2) = 0 ?
5h
4
= h + 2
h
4
= 2 ? h = 8?? 
 
Q6:  Fountains usually seen in gardens are generated by a wide pipe with an enclosure at one end 
having many small holes. Consider one such fountain which is produced by a pipe of internal 
diameter ?? ???? in which water flows at a rate ?? ????
-?? . The enclosure has 100 holes each of 
diameter ?? . ???? ???? . The velocity of water coming out of the holes is (in ????
-?? ): 
(A) 0.48 
(B) 96 
(C) 24 
(D) 48 
Ans: (D) Volume flow rate is same 
So ?? ( 1 × 10
-2
)
2
× 3 
 = 100 × ?? (
0.05 × 10
-2
2
)
2
× V
?? × 10
-4
× 3
 = 100 × ?? × 1/4 × 25 × 10
-8
× V
V =
4 × 3
25
× 100 = 48
 
 
 
 
 
 
 
Page 5


JEE Solved Example on Fluid Mechanics 
JEE Mains 
Q1:  The area of cross-section of the wider tube shown in figure is ?????? ????
?? . If a mass of ???? ???? is 
placed on the massless piston, the difference in heights ?? in the level of water in the two tubes is: 
 
(A) ???? ???? 
(B) ?? ???? 
(C) ???? ???? 
(D) ?? ???? 
Ans:  (C) Pressure due to difference in heights will be balanced by pressure due to 12 kg block 
 ? ???? h =
120
800 × 10
-4
10
4
 h =
120
800
× 10
4
 h =
12
80
=
3
20
 m = 15 cm
 
 
 
Q2:  Two cubes of size ?? . ?? ?? side, one of relative density 0.60 and another of relative density =
?? . ???? are connected by weightless wire and placed in a large tank of water. Under equilibrium the 
lighter cube will project above the water surface to a height of: 
(A) ???? ???? 
(B) ???? ???? 
(C) ???? ???? 
(D) Zero 
Ans: (B) 
 
Downward force on the cubes = ( ?? 1
+ ?? 2
) g 
 = ?? 1
???? + ?? 2
????
 ( 1750)× 10
 
Upward force on the cubes = ?? ( ?? 1
+ ?? ) ?? 
= 1000( h + 1)× 10 
Since cubes are in equilibrium 
So 17500 = 10000 ( h + 1) 
1.75 - 1 = h
 ? h = 0.75 m
 
 
 
Q3:  A cuboidal piece of wood has dimensions ?? , ?? and c. Its relative density is ?? . It is floating in a 
large body of water such that side a is vertical. It is pushed down a bit and released. The time 
period of SHM executed by it is: 
(A) ?? ?? v
??????
?? 
(B) ?? ?? v
?? ????
 
(C) ?? ?? v
????
????
 
(D) ?? ?? v
????
?? 
Ans: D 
 
Initially in equilibrium 
When pushed down by y distance, an extra upward force will act on the cube 
?? ( ?????? ) ?? = ???????????? [?? = ???????????????????????? of the cube] 
?? =
????
?? ?? ? ?? =
?? ????
?? ? ?? 2
=
?? ????
? ?? = v
?? ????
? ?? =
2?? ?? = 2?? v
????
?? 
 
Q4:  The frequency of a sonometer wire is ?? , but when the weights producing the tensions are 
completely immersed in water the frequency becomes ?? /?? and on immersing the weights in a 
certain liquid the frequency becomes ?? /?? . The specific gravity of the liquid is: 
(A) 
?? ?? 
(B) 
????
?? 
(C) 
????
????
 
(D) 
????
????
 
Ans: (D) ?? ? v ?? , ?? = tension in the wire in water frequency becomes f/2 ? Tension becomes 1/4 of 
the initial in liquid frequency becomes ?? /3 
 
? Tension become 1/9 of the initial 
For water ?? ? ?? =
3????
4
 
for liquid d?? Vg =
8
9
mg 
? ?? =
8
27
× 4 =
32
27
 
 
 
Q5:  A small ball of relative density 0.8 falls into water from a height of ?? ?? . The depth to which 
the ball will sink is (neglect viscous forces): 
(A) ?? ?? 
(B) ?? ?? 
(C) ?? ?? 
(D) ?? ?? 
Ans: (A) By work energy theorem 
?? water 
+ ?? gravity 
= ????? = 0
?? water 
= ( ?????? ) h
?? gravity 
= -( 0.8?? hg) ( h + 2)
 ? ?????? h - 0.8?????? ( h + 2) = 0
h - 0.8( h + 2) = 0 ?
5h
4
= h + 2
h
4
= 2 ? h = 8?? 
 
Q6:  Fountains usually seen in gardens are generated by a wide pipe with an enclosure at one end 
having many small holes. Consider one such fountain which is produced by a pipe of internal 
diameter ?? ???? in which water flows at a rate ?? ????
-?? . The enclosure has 100 holes each of 
diameter ?? . ???? ???? . The velocity of water coming out of the holes is (in ????
-?? ): 
(A) 0.48 
(B) 96 
(C) 24 
(D) 48 
Ans: (D) Volume flow rate is same 
So ?? ( 1 × 10
-2
)
2
× 3 
 = 100 × ?? (
0.05 × 10
-2
2
)
2
× V
?? × 10
-4
× 3
 = 100 × ?? × 1/4 × 25 × 10
-8
× V
V =
4 × 3
25
× 100 = 48
 
 
 
 
 
 
 
Q7: A vertical tank open at the top, is filled with a liquid and rests on a smooth horizontal surface. 
A small hole is opened at the centre of one side of the tank. The area of cross-section of the tank is 
?? times the area of the hole, where ?? is a large number. Neglect mass of the tank itself. The initial 
acceleration of the tank is: 
(A) 
?? ?? ?? 
(B) 
?? v ?? ?? 
(C) 
?? ?? 
(D) 
?? ?? v ?? 
Ans: (C) We know that force exerted by fluid coming out on the container is ???? ?? 2
 
?? = velocity of fluid 
?? =
v
2?? ?? 2
?? = area of the hole 
 Acceleration of the tank =
???? ?? 2
?? ( ?????? )
 =
?? ( AgH)
???????? =
?? ?? 
 
 
Q8:  Two water pipes ?? and ?? having diameters ?? × ????
-?? ?? and ?? × ????
-?? ?? , respectively, are 
joined in series with the main supply line of water. The velocity of water flowing in pipe ?? is: 
(A) 4 times that of ?? 
(B) 2 times that of ?? 
(C) ?? /?? times that of ?? 
(D) ?? /?? times that of ?? 
 Ans: (A) ?? 1
?? 1
= ?? 2
?? 2
?? ( 10
-2
)
2
?? ?? = ?? ( 2 × 10
-2
)
2
?? ?? ?? ?? = 4?? ?? 
 
 
Q9: A rectangular tank is placed on a horizontal ground and is filled with water to a height ?? above 
the base. A small hole is made on one vertical side at a depth D below the level of the water in the 
tank. The distance ?? from the bottom of the tank at which the water jet from the tank will hit the 
ground is: 
(A) ?? v?? ( ?? - ?? ) 
(B) ?? v ???? 
(C) ?? v?? ( ?? + ?? ) 
(D) 
?? ?? v ????