The Next Corridor

Kotdwara Uttarakhand

Academic Session 2023-2024

Roll No........................ Date........................
preparation exams 002

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Total Time: 3 Hrs 00 Mins Max Marks: 80

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General Instructions
attempt all questions

Standard/Class: 11th

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Subject: PHYSICS Volume 2

Section A

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1.
Objective(MCQ) - (1 Marks)

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Speed of a transverse wave on a straight wire (mass 6.0g, length 60cm and area of [1]
cross-section 1.0mm2) is 90 ms-1. If the Young’s modulus of wire is 16 × 1011 Nm-2,

2.
(a) 0.01 mm (b) 0.04 mm

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the extension of wire over its natural length is
(c) 0.03 mm (d) 0.02 mm
The elastic limit of brass is 379 MPa. What should be the minimum diameter of a
brass rod, if it is to support a 400 N load without exceeding its elastic limit?
[1]

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(a) 0.90mm

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(b) 1.00mm (c) 1.16mm (d) 1.36mm
In an experiment, brass and steel wires of length 1m each with areas of cross-
section 1mm2 are used. The wires are connected in series and one end of the
[1]

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combined wire is connected to a rigid support and other end is subjected to
elongation. The stress required to produce a net elongation of 0.2mm is [Take, the
Young’s modulus for steel and brass as 120 × 109Nm-2 and 60 × 109Nm-2,
respectively]
(a) 1.2 × 106 Nm-2 (b) 0.2 × 106 Nm-2
(c) 8 × 106 Nm-2 (d) 4.0 × 106 Nm-2
4. A steel wire having a radius of 2.0mm, carrying a load of 4kg, is hanging from a [1]
ceiling. Given that g = 3.1π ms-2, what will be the tensile stress that would be
developed in the wire?
(a) 6.2 × 106 Nm-2 (a) 5.2 × 106 Nm-2
(a) 3.1 × 106 Nm-2 (a) 4.8 × 106 Nm-2

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5. What will be the nature of flow of water from a circular tap, when its flow rate [1]
increased from 0.18 L/min to 0.48 L/min? The radius of the tap and viscosity of
water are 0.5cm and 10-3 Pa-s, respectively. (Take, density of water = 103kg/m3)
(a) Unsteady flow to steady flow (b) Remains steady flow
(c) Remains turbulent flow (d) Steady flow to unsteady flow
6. Wax is coated on the inner wall of a capillary tube and the tube is then dipped in [1]
water. Then, compared to the unwaxed capillary, the angle of contact q and the
height h upto which water rises change. These changes are
(a) q increases and h also increases
(b) q decreases and h also decreases
(c) q increases and h decreases (d) q decreases and h increases

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7. A solid sphere of radius R acquires a terminal velocity v1 when falling (due to gravity) [1]
through a viscous fluid having a coefficient of viscosityh. The sphere is broken into

when falling through the same fluid, the ratio (v1/v2) equals
(a) 9 (b) 1/27 (c) 1/9 (d) 27

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27 identical solid spheres. If each of these spheres acquires a terminal velocity, v2

8.

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A pendulum clock loses 12s a day, if the temperature is 40°C and gains 4s in a day, if [1]
the temperature is 20°C. The temperature at which the clock will show correct time
and the coefficient of linear expansion (a) of the metal of the pendulum shaft are,
respectively
(a) 25°C, a = 1.85 × 10-5/ºC
(c) 30°C, a = 1.85 × 10-3/ºC

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(b) 60°C, a = 1.85 × 10-4/ºC
(d) 55°C, a = 1.85 × 10-2/ºC
9.

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A pendulum made of a uniform wire of cross-sectional area A has time period T.
When an additional mass M is added to its bob, the time period changes TM. If the

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[1]

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Young’s modulus of the material of the wire is Y, then is equal to (g = gravitational
acceleration)

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10. Water flows in a horizontal tube (see figure). The pressure of water changes by
700Nm-2 between A and B, where the area of cross- section are 40cm2 and 20cm2,
respectively. Find the rate of flow of water through the tube. (Take, density of water =
[1]

1000 kgm-3)

(a) 3020 cm3/s (b) 2420 cm3/s

(c) 2720 cm3/s (d) 1810 cm3/s
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11. When the temperature of a metal wire is increased from 0°C to 10°C, its length [1]
increases by 0.02%. The percentage change in its mass density will be closest to
(a) 0.06 (b) 2.3 (c) 0.008 (d) 0.8
12. The pressure that has to be applied to the ends of a steel rod of length 10cm to keep [1]
its length constant when its temperature is raised by 100°C is (For steel Young’s
modulus is 2 × 1011 Nm-2 and coefficient of thermal expansion is 1.1 × 10-5 K-1)
(a) 2.2 × 108 Pa (b) 2.2 × 109 Pa
(c) 2.2 × 107 Pa (d) 2.2 × 106 Pa
13. The stress-strain graphs for two materials are shown in figure. (assume same scale). [1]

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(a) Material (i) is more elastic than material (ii) and hence material (ii) is more brittle.
(b) Materials (i) and (ii) have the same elasticity and the same brittleness.
(c) Material (ii) is elastic over a larger region of strain as compared to material (i).

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(d) Material (ii) is less brittle than material (i).
14. A copper wire of length 1.0m and a steel wire of length 0.5m having equal cross- [1]

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sectional areas are joined end-to-end. The composite wire is stretched by a certain
load which stretches the copper wire by 1mm. If the Young’s modulii of copper and
steel are respectively 1.0 × 1011 Nm-2 and 2.0 × 1011 Nm-2, the total extension of
the composite wire is
(a) 1.75 mm

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(b) 2.0 mm (c) 1.50 mm (d) 1.25 mm
15. A man grows into a giant such that his linear dimensions increase by a factor of 9.
Assuming that his density remains the same, the stress in the leg will change by a
[1]

factor of

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16. A uniform wire (Young's modulus 2 × 1011Nm-2) is subjected to longitudinal tensile [1]
stress of 5 × 107 Nm-2. If the overall volume change in the wire is 0.02%, the
fractional decrease in the radius of the wire is close to
(a) 1.0 × 10-4 (b) 1.5 × 10-4 (c) 0.25 × 10-4 (d) 5 × 10-4
17. Two different wires having lengths L1 and L2 and respective temperature [1]
coefficients of linear expansion a1 and a2, are joined end-to-end. Then the effective

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 temperature coefficient of linear expansion is

18. A sonometer wire of length 1.5m is made of steel. The tension in it produces an [1]
elastic strain of 1%. What is the fundamental frequency of steel, if density and
elasticity of steel are 7.7 × 103 kg/m3 and 2.2 × 1011 N/m2, respectively?
(a) 188.5 Hz (b) 178.2 Hz (c) 200.5 Hz (d) 770 Hz
19. A hollow spherical shell at outer radius R floats just submerged under the water [1]

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surface. The inner radius of the shell isr. If the specific gravity of the shell material is

with respect to water, then the value of r is

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20. If the ratio of lengths, radii and Young’s moduli of steel and brass wires in the figure [1]
are a b, and c respectively, then the corresponding ratio of increase in their lengths is

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21. A rod of length L at room temperature and uniform area of cross-section A, is made [1]
of a metal having coefficient of linear expansion a/°C. It is observed that an external
compressive force F, is applied on each of its ends, prevents any change in the length
of the rod, when its temperature rises by ΔT K. Young’s modulus Y for this metal is

22. A uniform cylindrical rod of length L and radius r, is made from a material whose [1]
Young’s modulus of elasticity equals Y. When this rod is heated by temperature T and
simultaneously subjected to a net longitudinal compressional force F, its length
remains unchanged. The coefficient of volume temperature expansion of the
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 material of the rod, is (nearly) equal to
(a) 9F/ (πr2 YT) (b) 6F/ (πr2 YT)
(c) 3F/ (πr2 YT) (d) F/ (3πr2 YT)
23. A boy’s catapult is made of rubber cord which is 42cm long, with 6 mm diameter of [1]
cross-section and of negligible mass. The boy keeps a stone weighing 0.02kg on it
and stretches the cord by 20cm by applying a constant force. When released the
stone flies off with a velocity of 20ms-1. Neglect the change in the area of cross-
section of the cord while stretched. The Young’s modulus of rubber is closest to
(a) 106 Nm-2 (b) 104 Nm-2 (c) 108 Nm-2 (d) 103 Nm-2
24. Two steel wires having same length are suspended from a ceiling under the same [1]
load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their
diameters is
(a) √2 : 1 (b) 1 : √2 (c) 2 : 1 (d) 1 : 2
25. A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage
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change in the length of the side of the cube is close to
(Take, Bulk modulus of metal, B = 8 × 1010 Pa)
(a) 1.67 (b) 0.6 (c) 20 (d) 5

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26. Young’s modulii is of two wires A and B are in the ratio 7 : 4. Wire A is 2m long and
has radius R. Wire B is 1.5m long and has radius 2mm. If the two wires stretch by the
same length for a given load, then the value of R is close to
[1]

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(a) 1.3 mm (b) 1.5 mm (c) 1.9 mm (d) 1.7 mm
27. On heating water, bubbles beings formed at the bottom of the vessel detach and rise. [1]

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Take the bubbles to be spheres of radius R and making a circular contact of radius r
with the bottom of the vessel. If r << R and the suface tension of water is T, value of r

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just before bubbles detach is (density of water is p)

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28. Water flows into a large tank with flat bottom at the rate of 10-4 m3 s-1. Water is also [1]
leaking out of a hole of area 1cm2 at its bottom. If the height of the water in the tank
remains steady, then this height is
(a) 4 cm (b) 2.9 cm (c) 5.1 cm (d) 1.7 cm

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 Section B

Subjective - (2 Marks)

29. [2]
What is the density of water at a depth where pressure is 80.0 atm, given that its
density at the surface is 1.03 × 103kg m-3?
30. [2]
A rod of length 1.05m having negligible mass is supported at its ends by two wires
of steel (wire A) and aluminium (wire B) of equal lengths as shown in Fig. The cross-
sectional areas of wires A and B are 1.0mm2 and 2.0mm2 , respectively. At what
point along the rod should a mass m be suspended in order to produce (a) equal
stresses and (b) equal strains in both steel and aluminium wires.

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31. [2]
A rigid bar of mass 15kg is supported symmetrically by three wires each 2.0m long.
Those at each end are of copper and the middle one is of iron. Determine the ratios

32.
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of their diameters if each is to have the same tension.

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The Marina trench is located in the Pacific Ocean, and at one place it is nearly eleven
km beneath the surface of water. The water pressure at the bottom of the trench is
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about 1.1 × 108 Pa. A steel ball of initial volume 0.32m3 is dropped into the ocean
and falls to the bottom of the trench. What is the change in the volume of the ball

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when it reaches to the bottom?

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33. [2]
A spring balance reads 10kg when a bucket of water is suspended from it. What is
the reading on the spring balance when:

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i. An ice cube of mass 1.5kg is put into the bucket?
ii. An iron piece of mass 7.8kg suspended by another string is immersed with half
its volume inside the water in the bucket (Relative density of iron = 7.8)?

34. [2]
Two wires of diameter 0.25cm, one made of steel and the other made of brass are
loaded as shown in Fig. The unloaded length of steel wire is 1.5m and that of brass
wire is 1.0m. Compute the elongations of the steel and the brass wires.

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35.
Explain why

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A spinning cricket ball in air does not follow a parabolic trajectory.
36.

and Cv.

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Define 1st law of thermodynamics. By using this law, derive relationship between Cp
[2]

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37. [2]
Consider an ideal gas with following distribution of speeds.

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Speed m/s 200 400 600 800 1000

% of molecules

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If all the molecules with speed 1000m/s escape from the system, calculate new
Vrms and hence T.
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38.

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i. Define critical velocity of liquid flow and state the factors affecting the critical
velocity of liquid.
[2]

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ii. Define terminal velocity. Establish an expression for it for a spherical body
falling through a viscous medium.

[2]

i. What is the phenomenon of capillarity? Derive an expression for the rise of

liquid in a capillary tube.
ii. What will happen if the length of the capillary tube is smaller than the height to
which the liquid rises? Explain briefly.

40. [2]
The wavelength corresponding to Emax for moon is 14 microns. Estimate the
temperature of moon.

Take b = 28.84 × 10-4 mK.

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41. [2]
A hole is drilled in a copper sheet. The diameter of the hole is 4.24cm at 27.0 °C.
What is the change in the diameter of the hole when the sheet is heated to 227°C?
Coefficient of linear expansion of copper = 1.70 × 10–5 K-1.
42. [2]
Calculate the stress developed inside a tooth cavity filled with copper when hot tea
at temperature of 57°C is drunk. You can take body (tooth) temperature to be 37°C
and a = 1.7 × 10-5/°C bulk modulus for copper = 140 × 109N/ m2
43. [2]

a. What is meant by thermal conductivity? What are the SI unit and CGS unit of
coefficient of thermal conductivity?

44.
b. Mention three applications of thermal conductivity in daily life.

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A thin rod having length L0 at 0°C and coefficient of linear expansion (alpha) has its

45.
new length.

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two ends maintained at temperatures (heta_1) and (heta_2,) respectively. Find its

What is viscosity? What are the factors affecting viscous force in a liquid flowing in a
[2]

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tube? Derive the relation for the velocity upto which the liquid can have streamlined
flow.

Write Kelvin-Planck and Clausius statements for second law of thermodynamics.

[2]

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Define coefficient of efficiency and coefficient of performance. Show the heat flow in
case of an engine and refrigerator using schematic diagrams.
47.

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The P-V diagram for a cyclic process is a triangle ABC drawn in order. The co-
ordinates of A, B, C are (4, 1), (2, 4) and (2, 1). The co-ordinates are in the order (P-V).

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Pressure is in Nm-2 and volume is in litre. Calculate work done during the process
[2]

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from A to B, B to C and C to A. Also, calculate work done in the complete cycle.

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48. [2]
State first law of thermodynamics. On the basis of this establish the relation
between two molar specific heats for an ideal gas.
49. [2]

a. What is an adiabatic process? Derive expression for the work done during such
process.

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 b. A refrigerator is to maintain eatable kept inside at 9°C. If the room temperature
is 36°C. Calculate the co-efficient of performance.

50. [2]

i. Define isothermal process. Derive an expression for work done during

isothermal process.
ii. A refrigerator is to remove heat from the eatables kept inside at 10°C. Calculate
the coefficient of performance if room temperature is 36°C.

51. [2]
Explain why.

52.
There is no atmosphere on moon.

A ballon has 5.0g mole of helium at 7°C. Calculate.

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a. The number of atoms of helium in the balloon,

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53.
b. The total internal energy of the system.

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i. Define mean free path.

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ii. Derive an expression for mean free path of a gas molecule.

54.

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i. Define viscosity. Write SI units of coefficient of viscosity.

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ii. Define terminal velocity. Establish an expression for it.
[2]

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T

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