QUESTION PAPER
PHYSICS
TIME: 3 HR
Note:
MARKS: 70
(i) All questions are compulsory.
(ii) Neat and well labelled diagrams must be drawn wherever necessary.
(iii) Figure to the right indicate full marks.
(iv) Use of only logarithmic table is allowed.
(v) All symbols have their usual meaning unless otherwise stated.
(vi) Answers to both the section must be written in the same answerbook.
(vii) Answer r\to every question must be written on a new page.
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SECTION- I
Q.1. Attempt any six:
[12]
(i) State the characteristics of angle of contact.
(ii) A body weighs 3.5 kg wt on the Earth. How much will it weigh on a planet whose mass and radius are
respectively 1/7th and ½ of those of the Earth?
(iii) Prove the relation 𝑣⃗ = 𝑤
⃗⃗⃗𝑥 𝑟⃗, where the symbols have their usual meanings.
(iv) A ballet dancer spins about a vertical axis through the centre of mass at 90 rpm with arms
outstretched. With the arms folded, the moment of inertia about the same axis of rotation changes by
25%. Calculate the new speed of rotation.
(v) Explain resonance with a resonance curve.
(vi) A soap fil,mm is formed between two straight parallel wired 5mm apart, each 10 cm long. Calculate the
work required to stretch the film by 1 mm.
[Surface tension of the soap water = 0.035N/m]
(vii) Derive an expression for the escape speed of a body from the surface of the Earth. Express it in terms
of the surface gravity.
(vii) 14 g of nitrogen occupy 0.25 m3 at 27°𝐶. Find the pressure exerted by the gas.
[Molar mass of nitrogen = 28g/mol, universal gas constant = 8.314J/mol.K]
Q.2. Attempt any three:
[9]
(i) Show that for small amplitude oscillations a simple pendulum performs linear SHM.
(ii)Two sound notes have wavelengths
70
149
𝑚 𝑎𝑛𝑑
70
151
𝑚 in air. Each of these produces 5 beats per second
with a third note. Calculate the speed of sound in air and frequencies of the three notes.
(iii) Derive an expression for the strain energy per unit volume of a stretched wire and show that it is equal
𝑦
to (tensile strain)2.
2
(iv) A conical pendulum has a bob of mass 0.2kg attached to a string 1 m long. If the angle made by the
string with the vertical is 10° , find (a) the tension in the string (b) the period of the circular motion of
the bob. [g = 9.8 m/s2]
Q.3. Attempt any one:
[7]
Assuming the expression for the pressure exerted by an ideal gas, prove that the kinetic energy per
3
molecule is 𝑘𝐵 𝑇, where 𝑘𝐵 is the Boltzmann constant and T is the absolute temperature of the gas. Hence
2
obtain an expression for the energy per mole of rigid diatomic molecules.
A pipe 30 cm long is open at both ends. Which harmonic mode of the pipe resonates with a 1.1 kHz sound
note? Will resonance be obtained with the same note if one end of the pipe is closed?
OR
Obtain an expression for the angular momentum of a rigid body rotating with a constant angular velocity.
The differential equation for a particle performing linear SHM is
1 𝑑2𝑥
4 𝑑𝑡 2
= -x.
If the amplitude of the motion is 5 cm and epoch is 𝜋/6 radian, write the expression for the displacement.
Also find the velocity of the particle when it is at x = +3 cm and travelling towards the mean position.
Q.4. Select and write the most appropriate answer from the given alternatives for each
subquestions:
[7]
(i) When 𝑛 drops of a liquid, each of radius r, coalesce to form a single drop, the radius of the large drop is
equal to ____________________ .
𝑟
(a) 3
√𝑛
3
(b) √𝑛. 𝑟
3
(c) √𝑛2 . 𝑟
(d) nr
(ii) The apparent frequency of sound heard by an observe is greater than the true frequency of the sound
emitted by a source. In this case, ______________________ .
(a) both the source and the observer move towards each other
(b) both the source and the observer move away from each other.
(c) the observer moves away from the stationary source
(d) the source moves away from the stationary observer
(iii) A particle executing linear SHM has velocities𝑣1 𝑎𝑛𝑑 𝑣2 at displacements 𝑥1 and 𝑥2 , respectively. The
period of oscillation of the particle is ______________________ .
(a)
1
𝑣12 −𝑣22
√
2𝜋 𝑥22 −𝑥 21
(b)
1
𝑥 2 −𝑥 2
𝑣 2 −𝑣 2
1
𝑥 2 −𝑥 2
(c) 2𝜋√𝑥 21−𝑥 22
√ 2 2
2𝜋 𝑣 2 −𝑣 2
1
2
(d) 2𝜋√𝑣22−𝑣 22
1
1
1
(iv) Two spheres of unequal radii have equal densities and are a distance greater than the sum of their radii
apart. If they are subject only to their mutual gravitational attraction, which of the following quantites
must have the same magnitude for both spheres?
(a) Initial acceleration
(b) Final velocity
(c) Force
(d) Gravitational acceleration due to one sphere at the surface of the other
(V) If the fundament frequency of a stretched wire is n, that of another wire opf the same material but
double the length and diameter is _______________ .
(a) 4n
(b) 2n
(c) n/√2
(d)n/4
(vi) Poisson’s ratio of a metal is about ______________ .
(a) -1
(b) 0
(c) 0.3
(d) 0.5
(vii) The equation of a stationary wave is y = 0.05 cos (2𝜋𝑥) sin(50𝜋𝑡), with all quantities in SI units. The
distance consecutive nodes is _____________ .
(a) 0.05m
(b) 0.5m
(c) 1m
(d) 2.5m
SECTION – II
Q.5. Attempt any six:
[12]
(i) What is the paramagnetic material? State Curie’s law for paramagnetism.
(ii) Find the longest wavelength in the Paschen series.
[Rydberg constant = 1.097 x 107 m-1]
(iii) Light of wavelength 6000 𝐴̇ is incident on a slit and the diffraction pattern is obtained on a screen
placed parallel to the s;lit 2m away. If the width of the central maximum is 8 mm, find the slit width.
(v) Draw a neat labelled circuit diagram of a full-wave rectifier using two diodes.
(vi) A bar magnet made of steel has magnetic moment 2.5A.m2 and mass 6.6 grams. Find the internsity of
magnetization of the bar magnet. [Density of steel = 7900 kg/m3]
(vii) Draw a neat labelled circuit diagram to study the characteristics of a transistor in common-emitter
configuration.
(viii) An 8 𝜇𝐹 capacitor is connected across a 200 V rms / 50 Hz ac supply. What is the peak voltage across
the capacitor?
Q.6. Attempt any three:
(i) State and prove Gauss’s theorem in electrostatics.
(ii) The photoelectric work function of molybdenum is 4.2 eV. Find (A) the threshold wavelength for
molybdenum (b) the stopping potential for photoelectrons emitted with maximum kinetic energy of
0.772 eV. [speed of light in free space = 3 x 108 m/s, planck constant = 6.63 x 10-34 J.s, electron charge =
1.602 x 10-19C]
(iii) Explain Doppler effect in light. Hence explain the red and blue shifts.
(iv) A galvanometer with a coil of resistance 14𝛺 givesw full scale deflection for a current of 5 mA. To extend
its range up to 4 A, the only shunt available is 0.02𝛀. What resistance should be connected in series with
the coil?
Q.7. Attempt any one:
[9]
Derive an expression for the energy of the electron in a stationary orbit in the hydrogen atom. Hence,
show that the energy is inversely proportional to the radius of the orbit and the square of the principal
quantum number.
A current of 1 A passes through a coil when 100 V dc is applied across it . But when an ac voltage of 100 V
rms/50 Hz is applied, the current is only 0.5A. Calculate the resistance, impedance and self-inductance of
the coil.
OR
Assuming the conditions for the path difference between two interfering light waves for bright and dark
fringes. Obtain an expression for the fringe width. Hence, show that the bright and dark fringes are equally
spaced.
A potentiometer wire 4 m long has a resistance of 4𝛀. What resistance must be connected in series with
the wire and a cell of emf 2V having internal resistance of 2𝛀 to get potential drop of 10-3 V/m along the
wire?
Q.8. Select and write the most appropriate answer from the given alternatives for each
subquestions:
[7]
(i) A ray of light passes from a medium of refractive index n into vacuum. The angle of refraction is twice the
angle of incidence. For this case, the angle of incidence is ___________________ .
(a) cos-1 n/2
(b) 2 cos-1 n/2
(c) ½ cos-1 n
(d) 2 cos-1 n
(ii) The SI unit of magnetic flux density is _______________________ .
(a) The tesla
(b) the weber
(c) the weber per metre (d) the volt. Second
(iii) A device that converts a nonelectrical; signal into an electrical signal or vice versa is called _______________ .
(a) a transmitter
(b) a modulator
(c) a rectifier
(d) an electrical transducer
(iv) Which of the following molecules is nonpolar?
(a) N2O
(b) CO2
(c) H2O
(d) HCL
(v) Electrons are ejected from a metallic surface on;ly when incident radiation has certain minimum
_________________ .
(a) wavelength
(b) frequency
(c) intensity
(d) amplitiude
(vi) Kiechhoff’s junction law is equivalent to the conservation of ____________________ .
(A) electric potential (b) electric flux
(c) charge
(d) energy
(vii) A very long solenoid has 8400 windings and a length of 7 m. If the field inside is 2𝜋 x 10-3 T, the current
in the windings is about __________________ .
(a) 8.3 A
(b) 4.2 A
(c) 0.83 A
(d) 0.42A