NAVRACHANA HIGHER SECONDARY SCHOOL MARKS: 70

FINAL EXAMINATION DATE: 26/02/24

XI (2023-24) TIME: 3 HRS.
PHYSICS (042)

GENERAL INSTRUCTIONS:
i. There are 33 questions in all. All questions are compulsory
ii. This question paper has five sections: Section A, Section B, Section C, Section D and
Section E. All the sections are compulsory.
iii. Section A contains sixteen questions of 1 mark each, Section B contains five questions
of two marks each, Section C contains seven questions of three marks each, section D
contains three long questions of five marks each and Section E contains two case study-
based questions of 4 marks each.
iv. There is no overall choice. However, an internal choice has been provided in section B,
C, and D. You have to attempt only one of the choices in such questions.
v. Use of calculators is not allowed.

SECTION - A
1. The horizontal range of a projectile fired at an angle of 15° is 50 m. If it is fired (1)
at the same speed at an angle of 45°, its range will be
(a) 60 m (b)71 m (c)100 m (d)141 m
2. Two equal vectors have their resultant equal to either of them. At what angle are (1)
they inclined to each other?
(a)90 (b) 120 (c) 180 (d) 60
3. From a fountain, water is sprayed in all directions with same speed V. Find the (1)
maximum area of the ground where water is spread.
(a) πV4/g2 (b) πV2/g (c) g/πV4 (d) πV2/g2
4. A shell explodes into three fragments of equal masses. Two fragments fly off at (1)
right angles to each other with speeds of 9 ms–1 and 12 ms–1. What is the speed
of the third fragment?
(a) 9 ms–1 (b) 12 ms–1 (c) 15 ms–1 (d) 18 ms–1
5. Two billiard balls each of mass 50 g, moving in opposite directions each with a (1)
speed 6 ms–1, collide and rebound with the same speed. The impulse imparted
to each ball due to the other is
(a) 0.3 Ns (b) 0.6 Ns (c) 0.9 Ns (d) 1.2 Ns
6. A block of mass 10 kg is suspended through two light spring (1)
balances as shown in figure.
(a) Both the scales will read 10 kg.
(b) Both the scales will read 5 kg.
(c) The upper scale will read 10 kg and the lower zero.
(d) The readings may be anything but their sum will be10 kg.

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 7. A coin placed on a rotating turntable just slips if it is placed at a distance of 4 (1)
cm from the centre. If the angular velocity of the turntable is doubled, it will just
slip at a distance of
(a) 1 cm (b) 2 cm (c) 4 cm (d) 8 cm
8. A molecule consists of two atoms, each of mass m, separated by a distance a. (1)
The moment of inertia of the molecule about its centre of mass is
(a) 2 ma2 (b) ma2 (c) 1/2 ma2 (d) 1/4 ma2
9. If the distance of the Earth is halved from the Sun, then the number of days in (1)
a year will be
(a) 129 (b) 730 (c) 182.5 9 (d) 365
10. The displacement of a simple harmonic oscillator after 3 seconds starting from (1)
its mean position is equal to half of its amplitude. The time period of its harmonic
motion is
(a) 6 s (b) 8 s (c) 12 s (d) 36 s
11. The time period of a satellite orbiting Earth in a circular orbit is independent of (1)
_________________________
(a) radius of the orbit
(b) the mass of the satellite
(c) both the mass and radius of the orbit
(d) neither the mass nor the radius of its orbit
12. Two uniform brass rods A and B of lengths l and 2l and radii 2r and r, (1)
respectively are heated to the same temperature. The ratio of the increase in the
length of A to that of B is
(a) 1 : 1 (b) 1 : 2 (c) 1 : 4 (d) 2 : 1
13. 300 g of water at 25°C is added to 100 g of ice at 0°C. The final temperature of (1)
the mixture is
(a) – 5/3 °C (b) – 5/2 °C (c) – 5 °C (d) 0 °C
14. Two identical waves, each of frequency 10 Hz, are travelling in opposite (1)
directions in a medium with a speed of 20 cms–1. The distance between adjacent
nodes is
(a) 1.0 cm (b) 1.2 cm (c) 1.5 cm (d) 2.0 cm
15. A hospital uses an ultrasonic scanner of frequency 3.2 MHz. What is the (1)
wavelength of ultrasonic waves in a tissue in which the speed of the waves is 1.6
km s–1?
(a) 0.25 mm (b) 0.5 mm (c) 0.75 mm (d) 1 cm
16. A pipe of length 20 cm is closed at one end. Which harmonic mode of the pipe is (1)
resonantly excited by a 425 Hz source? The speed of sound = 340 ms–1.
(a) First harmonic (b) Third harmonic (c) Fifth harmonic (d) None

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 SECTION - B
17. Derive the relation for the maximum height attained by a projectile fired at an (2)
angle 𝜃 with the horizontal.
OR
Show that the trajectory of a projectile is a parabola.
18. Express the first law of thermodynamics mathematically. Mention the terms (2)
involved.
19. A particle executing linear SHM has a maximum velocity of 40 cm/s and a (2)
maximum acceleration of 50 cm/s2. Find its amplitude and period of oscillation.
20. A rope is wound around a hollow cylinder of mass M = 3 kg and radius R = 40 (2)
cm. If the rope is pulled with a force F = 30 N, find (a) the angular acceleration
of the cylinder and (b) the linear acceleration of the rope. MI of the cylinder about
its axis = MR2.
21. When a plane wave travels in a medium, the displacements of particles are given (2)
by, 𝑦 = 0.01 𝑠𝑖𝑛 (80 𝑥 − 3𝑡), where 𝑥 and 𝑦 are in metre and 𝑡 in second. Find the
(a) wavelength (b) velocity of the wave
SECTION - C
22. A bullet of mass 0.02 kg is moving with a speed of 10 m/s. It can penetrate 10 (3)
cm of a wooden block, and comes to rest. If the thickness of the target would
be 6 cm only find the KE of the bullet when it comes out.
23. Eight rain drops of radius 1mm each falling with terminal velocity 5 cm/s (3)
coalesce to form a bigger drop. Find the terminal velocity of a bigger drop.
OR
A liquid drop of diameter 4mm breaks into 1000 droplets of equal size. Calculate
the resultant change in surface energy, the surface tension of the liquid is 0.07
N/m.
24. (a) Write the condition for a system to be in equilibrium. (3)
(b) A body of mass m is suspended by two strings making
angles 𝛼 =30o and 𝛽 =60o with the horizontal. Find the
tension in the strings.

25. Obtain the relation between torque and angular momentum. Using the same, (3)
state the law of conservation of angular momentum.
26. (a) Define the term ‘coefficient of linear expansion’ (3)
(b) Obtain its relation with the coefficient of volume expansion.
27. Derive the relation for the pressure exerted by an ideal gas on the walls of a (3)
container.
28. (a) What are standing waves and how are they produced ? (3)
(b) Obtain the displacement relation for a standing wave on a string of length

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 L and hence explain the formation of nodes and anti-nodes.
(c) Draw diagrams showing the first two modes of vibration.
SECTION - D
29. (a) What do you understand by escape velocity? Derive an expression for it in (5)
terms of the parameters of a given planet.
(b) A satellite is revolving in a circular orbit around the earth with a speed equal
to half of the escape speed from the earth of radius R. What is the height of the
satellite above the surface of the earth?
OR
(a) How does the value of g change with the increase of depth? Obtain the
mathematical expression for the same and show that the value of g at the center
of the earth is zero.
(b) At what depth the weight of the body be 1/3 times that on the surface of the
earth?
30. (a)Hydraulic lift is a device used to lift heavy loads. State the principle behind (5)
the working of the device.
(b) The speed of the outflow of a liquid from an open tank is identical to that of
a freely falling body. Obtain the relation for the speed of outflow (efflux) using
Bernoulli’s principle.
OR
Washing with water does not remove grease stains from clothes but the addition
of detergent removes the molecules of greasy substances.
a) Which property of a liquid causes the above effect?
b) A single drop of liquid is split into 8 identical drops. What will be the excess
pressure in each drop?
c) How can the coefficient of viscosity of a highly viscous liquid be determined
by Stokes’ method?
31. (a) Find the total kinetic energy of the particle executing SHM. And show (5)
graphically variation of P.E. and K.E. with time in SHM.
(b) What is the ratio between the potential energy and total energy of a particle
executing SHM, when its displacement is half of its amplitude?
OR
(a) Prove that a simple pendulum executes SHM and find the relation for its
time period.
(b) The amplitudes of oscillations of two simple pendulums similar in all
respects are 2 cm and 5 cm respectively. Find the ratio of their energies of
oscillations.

SECTION - E

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32. There are many types of spring. Important among these are helical and spiral (4)
springs as shown in the figure.

Usually, we assume that the springs are massless. Therefore, work done is
stored in the spring in the form of elastic potential energy of the spring. Thus,
the potential energy of a spring is the energy associated with the state of
compression or expansion of an elastic spring.
(i) The ratio of spring constants of two springs is 2 : 3. What is the ratio of
their potential energy, if they are stretched by the same force?
(a) 2 : 3 (b) 3 : 2 (c) 4 : 9 (d) 9 : 4
(ii) The potential energy, i.e., U(x) can be assumed zero when
(a) x = 0 (b) gravitational force is constant
(c) infinite distance from the gravitational source
(d) All of the above
(iii) The potential energy of a body is increases in which of the following
cases?
(a) If work is done by a conservative force
(b) If work is done against conservative force
(c) If work is done by a non-conservative force
(d) If work is done against non-conservative force
(iv) The potential energy of a spring increases by 15 J when stretched by 3
cm. If it is stretched by 4 cm, the increase in potential energy is
(a) 27 J (b) 30 J (c) 33 J (d) 36 J

33. The graph shown below shows (4)

qualitatively the relation between the
stress and the strain as the deformation
gradually increases. Within Hooke’s limit
for a certain region stress and strain
relation is linear. Beyond that up to a
certain value of strain the body is still
elastic and if deforming forces are
removed the body recovers its original
shape.

(i) If deforming forces are removed up to which point the curve will be
retraced?

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 (a) upto OA only (b) upto OB (c) upto C (d) Never retraced its path
(ii) In the above question, during loading and unloading the force exerted by
the material are conservative up to
(a) OA only (b) OB only (c) OC only (d) OD only
(iii) During unloading beyond B, say C, the length at zero stress in now equal
to
(a) less than original length (b) greater than original length
(c) original length (d) can’t be predicted
(iv) Substances which can be stretched to cause large strains are called
(a) isomers (b) plastomers (c) elastomers (d) polymers

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