PHYSICS
Class : XII (AN) Target IIT JEE 2013 UID Q.1
Q.2
MECHANICS
[SINGLE CORRECT CHOICE TYPE] A con conee of heig height ht 1m and and half half angl anglee 45 45 ° is kept inside a tank. Both the surfaces are perfectly smooth so that no air is trapped in between the base of the cone and the bottom of the tank. Then the tank is filled with water upto height of 1m.(Take P atm = 1 × 105 Pa, Density Densi ty of water = Average Average density 3 3 of the cone = 10 kg/m ) Find the normal reaction exerted by the tank on the cone. (A) zero (B) ! × 104 N (C) 1.1! × 104 N (D) 1.1! × 105 N A closed closed hemis hemispher pherica icall shell shell of radiu radiuss R is filled filled with fluid at unifor uniform m pressur pressuree p. The net net force force of the fluid fluid on the curved portion portio n of the shell is given by: 2 (A) 2!R p (B) !R2p (C) 4!R2p (D) (4/3)!R2p Paragraph for question nos. 3 to 4 The figure below shows four situations situation s in which a gray liquid and a black liquid (which we known nothing nothin g about) are in a U tube.
Q.3
Which Which of the follow following ing situati situations ons does does not not show show static static equilib equilibriu rium m of liquids liquids.. (A) I (B) II (C) III (D) IV
Q.4
In which which of of the follow following ing situati situation(s on(s)) of static static equilib equilibrium rium must must the the density density of the gray gray liquid liquid be great greater er than the density of the black liquid? li quid? (circle all appropriate cases) (A) I (B) II (C) III (D) IV
Q.5
A plastic plastic ball ball is drop dropped ped in water water from from a height height of of 45m. 45m. It goes goes in in the water water and then then bounc bounces es back back to to the starting point. (Neglect viscosity). v iscosity). If the time taken in this process is 18seconds than tha n the specific gravity of the material of plastic ball is (A) 0.33 (B) 0.5 (C) 0.67 (D) 0.75
Q.6
A balloon fille lled with 1 m3 of hydrogen at atmospheric pressure can lift how much more weight than when filled with 1 m3 of helium at atmospheric pressure? (Take average molecular weight of the air as 28 g/mol and neglect mass of balloon material) (A) 13/12 times
(B) 2 times
(C) 12/13 times
(D) half
Q.7
A cubica cubicall block block of wood wood of specifi specificc gravit gravity y 0.5 and and chunk chunk of concr concrete ete of spec specific ific grav gravity ity 2.5 are are fastene fastened d together. together. The ratio of mass of wood to the mass of concrete which makes the combination to float with entire volume of the combination submerged subm erged in water is (A) 1/5 (B) 1/3 (C) 3/5 (D) 2/5
Q.8
An iceber iceberg g is floati floating ng in ocea ocean. n. What What fractio fraction n of its volum volumee is above above the the water water ? (Given (Given : density density of ice = 3 3 900 kg/m and density of ocean water = 1030 kg/m ) (A)
90 103
(B)
13 103
(C)
10 103
(D)
1 103
[1]
Q.9
A stone tied to a string is supported from a spring scale that read 10N. A pail of water rests on a platform scale that reads 80N. The stone is lowered into the water, and the spring scale then reads 5N. It follows that the platform scale. (A) still reads 80 N (B) now reads 70 N (C) now reads 90 N (D) now reads 85 N
Q.10
Two spheres of volume 250 cc each but of relative densities 0.8 and 1.2 are connected by a string and the combination is immersed in a liquid in vertical position as shown in figure. The tension in the string is (g = 10 m/s2) (A) 5.0 N
(B) 0.5 N
(C) 1.0 N
(D) 2.0 N
Q.11
When submerged under water, the mass of one cubic centimeter of pure gold is 18.3 g. What would be its mass in air? (A) 16.3 g (B) 17.3 g (C) 18.3 g (D) 19.3 g (E) 20.3 g
Q.12
An object of specific gravity " is hung from a massless string. The tension in the string is T. The object is immersed in water so that one half of its volume is submerged. The new tension in the string is (A)
( 2" ) 1 % && ##T ' 2" $
(B)
( 2" * 1 % && ##T ' 2" $
(C)
( " * 1 % && ##T ' " $
(D)
( " ) 1 % && ##T ' " $
Q.13
A heavy brass sphere is hung from a light spring and is set in vertical small oscillation with a period T. The sphere is now immersed in a non-viscous liquid with a density 1/10th the density of the sphere. If the system is now set in vertical S.H.M., its period will be (A) (9/10)T (B) (9/10) 2T (C) (10/9) T (D) T
Q.14
A hydraulic press has one piston of diameter 2.0 cm and the other piston of diameter 8.0 cm. What force must be applied to the smaller piston to obtain a force of 1600N at the larger piston? (A) 6.25N (B) 25N (C) 100 N (D) 400N (E) 1600N
Q.15
The diagram shows a pipe of uniform cross section in which water is flowing. The directions of flow and the volume flow rates (in cm 3 /s) are shown for various portions of the pipe. The direction of flow and the volume flow rate in the portion marked A are:
+ and 3 cm3 /s (E) + and 15 cm 3 /s (A)
(B)
, and 7 cm3 /s
(C)
+ and 9 cm3 /s
(D)
, and 11 cm3 /s
Q.16
Water flows into a cylindrical vessel of large cross-sectional area at a rate of 10 – 4 m3 /s. It flows out from a hole of area 10 – 4 m2, which has been punched through the base. How high does the water rise in the vessel? (A) 0.075 m (B) 0.051 m (C) 0.031 m (D) 0.025 m
Q.17
A horizontal jet of water having velocity = 10m/s and stream cross section = 2cm 2 hits a stationary flat plate perpendicularly with the water splashing out parallel to the plate. The plate experiences a force of (A) 40N (B) 20N (C) 8N (D) 10N
Q.18
An L-shaped pipe is lowered into a river such that the horizontal arm of the pipe is parallel to the river flow velocity and its open end points upstream. The river flow velocity = 5 m/s. To what height above the surface of water will the water rise in the vertical arm of the pipe? (A) 1.25 m (B) 5 m (C) 10 m (D) None
[2]
Q.19
A bent tube is lowered into water stream as shown in the figure. The velocity of the stream relative to the tube is equal to V = 2 m/s. The closed upper end of the tube located at height h 0 = 10 cm above free surface of water has a small orifice. To what height h will the water get spurt?
(A) 5 cm
(B) 10 cm
(C) 20 cm
(D) 40 cm
Q.20
A liquid flows through a tube of uniform cross-section on horizontal plane as shown. Direction of the force exerted by the liquid on the tube is towards (A) East (B) South (C) North-West (D) North-East
Q.21
A cylindrical vessel filled with water upto the height H becomes empty in time t 0 due to a small hole at the bottom of the vessel. If water is filled to a height 4H it will flow out in time (A) t0 (B) 4t0 (C) 8t0 (D) 2t0
Q.22
Q.23
[REASONING TYPE] A block of ice on earth floats on water with 9/10 of its volume submerged. Statement -1 : On moon the block of ice would float on water with less than 9/10 of its volume submerged. Statement -2 : The acceleration due to gravity on moon surface is less than that on earth. (A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1. (B) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1. (C) Statement-1 is true, statement-2 is false. (D) Statement-1 is false, statement-2 is true. [MATRIX TYPE] In the table shown below, column-II shows the possible outcomes to the water level of a swimming pool when a person standing on a boat in it does any one of the actions shown in column-I. Match the possible outcomes. Column-I
Column-II
(A)
He throws a 20 kg iron anchor from the boat into the water, which then settles at the bottom.
(P)
It becomes lower
(B)
He throws out a 20 kg log from the boat. The log floats on water
(Q)
It becomes higher.
(C)
He empties 20 kg of water from the boat into the pool.
(R)
It stays the same.
(S)
Cannot be predicted from the information given.
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[SUBJECTIVE TYPE] Q.24
(i) (ii)
A monometer reads the pressure of a gas in a enclosure as shown in figure (a). When some of the gas is removed by a pump, the manometer reads as in (b). The liquid used in the manometers is mercury and the atmospheric pressure is 76 cm of mercury.
(a) (b) Give the absolute and guage pressure of the gas in the enclosure for cases (a) and (b) in units of cm of mercury. How would the levels change in case (b) if 13.6 cm of water are poured into the right limb of the manometer.
Q.25
A closed tube in the form of an equilateral triangle of side l contains equal volumes of three liquids which do not mix and is placed vertically with its lowest side horizontal . Find x in the figure if the densities of the liquids are in A.P.
Q.26
The cross-sectional area of the U-tube shown in the fig. is everywhere uniform and of value 1.25 × 10 – 3 m2. The horizontal section of the tube is of length 20 cm. When at rest, the limbs of the tube contain a liquid of density 2.5 up to equal heights. If the tube is rotated with angular velocity of 8.4 rad/sec about one limb, calculate the volume of liquid that flows from one limb to the other.
Q.27
A cube of wood supporting 200 g mass just floats in water. When the mass is removed, the cube rises by 2 cm. What is the size of the cube?
Q.28
We have two liquids of different densities. A force of 1.36 N can hold the same piece of metal in one of them, and of 0.82 N in the other. In what volume proportion should they be mixed so that the holding force is exactly 1 N?
Q.29 (a) (b)
A rod of length 6m has a mass 12 kg. It is hinged at one end at a distance of 3m below water surface . What weight must be attached to the other end of the rod so that 5m of the rod is submerged. Find the magnitude and direction of the force exerted by the hinge on the rod. (specific gravity of the rod is 0.5)
Q.30
A block of ice with an area of cross section A and a height h floats in water of density "0. What work should be performed to submerge the ice block completely into water if density of ice is "1?
[4]
Q.31
A hole in the horizontal bottom of the container is closed by a hemispherical cap of radius R (see figure). The vessel is filled with liquid of density d. Bottom is at a depth of H. Find the force with which the cap presses down on the bottom of the vessel. Neglect atmospheric pressure. If the force is a ! N, fill 'a' in the OMR sheet. (Take : d = 10 3 kg/m3, H = 1m, R = 30 cm)
H R
Q.32
A rectangular tank of height 10m filled with water, is placed near the bottom of an incline of angle 30°. At height x from bottom a small hole is made as shown figure such that the stream coming out from hole, strikes the inclined plane normally. Find x.
Q.33
(i)
A cylindrical tank having cross-sectional area A = 0.5 m 2 is filled with two liquids of densities "1 = 900 kgm – 3 & "2 = 600 kgm – 3, to a height h = 60cm as shown in the figure. A small hole having area a = 5 cm 2 is made in right vertical wall at a height y=20cm from the bottom. Calculate velocity of efflux.
(ii)
horizontal force F to keep the cylinder in static equilibrium, if it is placed on a smooth horizontal plane.
(iii)
minimum and maximum value of F to keep the cylinder at rest. The coefficient of friction between cylinder and the plane is - = 0.01.
(iv)
velocity of the top most layer of the liquid column and also the velocity of the boundary separating the two liquids.
Q.3 4 A siphon tube is discharging a liquid of specific gravity 0.9 from a reservoir as shown in fig. find (a) find the velocity of the liquid coming out of sipho n at D (b) find the pressure at the highest point B (c) find the pressure at point C, here g = 10 m/s 2.
[5]
Q.1
D
Q.2
B
Q.3
B
Q.4
D
Q.5
C
Q.6
A
Q.7
C
Q.8
B
Q.9
D
Q.10
B
Q.11
C
Q.12
B
Q.13
D
Q.14
C
Q.15
E
Q.16
B
Q.17
B
Q.18
A
Q.19
B
Q.20
D
Q.21
D
Q.22
D
Q.23
(A) P (B) R (C) R
Q.24
(i) absolute pressure = 96 cm of Hg, (ii) Gauge pressure = 20 cm of Hg for (a) (iii) Mercury would rise in the left limb such that the difference in the levels in the two limbs becomes 9 cm
Q.25
Q.29
Q.32
x = 1/3
Q.26
(a) 7/3 kg, (b) 170/3 N
25 3
m
Q.33
88.2 c.c
Q.27
Q.30
a = 10 cm
Q.28
Agh 2 ("0 * "1 ) 2 2" 0
v1 v2
.
1 2
Q.31
720
(i) 4m/s, (ii) F = 7.2N, (iii) Fmin = 0, Fmax = 52.2 N, (iv) both 4 × 10 – 3 m/s
Q.34 (a) 10 m/sec, (b) 4.15×10 4Pa, (c) 6.4 × 10 4 Pa
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