Physics 2009 Set 1 Close Subjective Test (i) All questions are compulsory. (ii) There are 30 questions in total. Questions 1 to 8 carry one mark each, Questions 9 to 18 carry two marks each, Question 19 to 27 carry three marks each and Question 28 to 30 carry five marks each. (iii) There is no overall choice. However, an internal choice has been provided. (iv) Wherever necessary, the diagrams drawn should be neat and properly labelled. (v) Use of calculators is not permitted. Question 1 ( 1.0 marks) What is sky wave propagation? Solution: They type of propagation in which radio waves are transmitted towards the sky and are reflected by the ionosphere towards the desired location on earth is called sky wave propaga tion. Question 2 ( 1.0 marks) Write the following radiations in ascending order with respect to their frequencies: X-rays, microwaves, UV rays and radio waves. Solution: The given radiations can be arranged in ascending order with respect to their frequencies as: Radio waves < Microwaves < UV rays < X-rays Question 3 ( 1.0 marks)
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(iii) There is no overall choice. However, an internal choice has been provided.
(iv) Wherever necessary, the diagrams drawn should be neat and properly labelled.
(v) Use of calculators is not permitted.
Question 1 ( 1.0 marks)
What is sky wave propagation?
Solution:
They type of propagation in which radio waves are transmitted towards the sky and are reflected by the ionosphere towards the desired location on earth is called sky wave propagation.
Question 2 ( 1.0 marks)
Write the following radiations in ascending order with respect to their frequencies:
X-rays, microwaves, UV rays and radio waves.
Solution:
The given radiations can be arranged in ascending order with respect to their frequencies as:
Magnetic field lines can be entirely confined within the core of a toroid, but not within a straight
solenoid. Why?
Solution:
Magnetic field lines form closed loops around a current-carrying wire. The geometry of astraight solenoid is such that magnetic field lines cannot loop around circular wires without
spilling over to the outside of the solenoid. The geometry of a toroid is such that magnetic field
lines can loop around electric wires without spilling over to the outside. Hence, magnetic fieldlines can be entirely confined within the core of a toroid, but not within a straight solenoid.
Question 4 ( 1.0 marks)
You are given following three lenses. Which two lenses will you use as an eyepiece and as an
objective to construct an astronomical telescope?
Lens Power (P) Aperture (A)
L1 3D 8 cm
L2 6D 1 cm
L3 10D 1 cm
Solution:
For constructing an astronomical telescope, the objective should have the maximum diameter. Of
the three lenses given, L1 has the maximum diameter.
The eyepiece should have the highest power for better magnification. Therefore, we use lens L3.
Question 5 ( 1.0 marks)
If the angle between the pass axis of polarizer and the analyser is 45º, write the ratio of the
intensities of original light and the transmitted light after passing through the analyser.
Solution:
I = Im cos
2
θ
Where,
I is the transmitted intensity
I mis the maximum value of the transmitted intensity
Nuclear density is independent of mass number. Hence, both the atoms have the same nuclear
density.
Question 9 ( 2.0 marks)
A cell of emf ‘ E ’ and internal resistance ‘r ’ is connected across a variable resistor ‘ R’. Plot agraph showing the variation of terminal potential ‘V ’ with resistance R. Predict from the graph
the condition under which ‘V ’ becomes equal to ‘ E ’.
Solution:
V becomes equal to E when no current flows through the circuit.
The condition under which V will be equal to E is when R = ∞
Question 10 ( 2.0 marks)
(i) Can two equi-potential surfaces intersect each other? Give reasons.
(ii) Two charges −q and +q are located at points A (0, 0, −a) and B (0, 0, +a) respectively. Howmuch work is done in moving a test charge from point P (7, 0, 0) to Q (−3, 0, 0)?
Solution:
(i) Two equipotential surfaces cannot intersect each other because when they will intersect, the
electric field will have two directions, which is impossible.
(ii) Charge P moves on the perpendicular bisector of the line joining +q and −q. Hence, this perpendicular bisector is equidistant from both the charges. Thus, the potential will be same
everywhere on this line. Therefore, work done will be zero.
How does a charge q oscillating at certain frequency produce electromagnetic waves?
Sketch a schematic diagram depicting electric and magnetic fields for an electromagnetic wave
propagating along the Z-direction.
Solution:
An oscillating charge is an example of accelerated charge. We know from Maxwell’s theory thataccelerated charge radiates electromagnetic waves. These electromagnetic waves are produced
because oscillating charge produces oscillating magnetic field, which in turn produces an
oscillating electric field. This process goes on, giving rise to an electromagnetic wave.
Question 14 ( 2.0 marks)
A charge ‘q’ moving along the X- axis with a velocity is subjected to a uniform magnetic fieldB along the Z-axis as it crosses the origin O.
(i) Trace its trajectory.
(ii) Does the charge gain kinetic energy as it enters the magnetic field? Justify your answer.
Solution:
(i)
The direction of magnetic field is along the negative X-direction. Hence, the magnetic force willact in such a way that this particle describes a circular motion as shown below.
The graph of electric field E (r ) with distance r from the centre of the shell for 0 ≤ r ≤ ∞.
Question 20 ( 3.0 marks)
Three identical capacitors C1, C2 and C3 of capacitance 6 μF each are connected to a 12 V batteryas shown.
Find
(i) charge on each capacitor
(ii) equivalent capacitance of the network
(iii) energy stored in the network of capacitors
Solution:
The 12 V battery is in parallel with C 1 , C 2, and C 3. C 1 and C 2are in series with each other whileC 3 is in parallel with the combination formed by C 1 and C 2.
For maximum wavelength, energy transition should be minimum.
A undergoes minimum energy transition.
A = 2 eV
Thus, photon in A will have the maximum wavelength.
Question 22 ( 3.0 marks)
A proton and an alpha particle are accelerated through the same potential. Which one of the twohas (i) greater value of de Broglie wavelength associated with it, and (ii) less kinetic energy?Justify your answers.
Solution:
Kinetic energy gained by the proton = eV
Kinetic energy gained by the alpha particle = 2eV
Let v1 be the velocity of the proton and v2 be the velocity of the alpha particle.
The figure shows experimental set up of a meter bridge. When the two unknown resistances Xand Y are inserted, the null point D is obtained 40 cm from the end A. When a resistance of 10 Ω
is connected in series with X, the null point shifts by 10 cm. Find the position of the null pointwhen the 10 Ω resistance is instead connected in series with resistance ‘Y’. Determine the values
1 ampere is the value of that steady current which when maintained in each of the two very long,
straight, parallel conductors of negligible cross section and placed one metre apart in vacuum,would produce on each of these conductors a force equal to 2 × 10−7 Newton per metre of length.
OR
Cyclotron is a machine used to accelerate charged particles or ions to high energies. It uses both
electrical and magnetic fields in combination to increase the speed of the charged particles.
The particles move in two semi-circular containers D1 and D2, called Dees. Inside the metal box,the charged particle is shielded from external electric fields.
When the particle moves from one dee to another, electric field is acted on the particle.
The sign of the electric field is changed alternately, in tune with the circular motion of the
particle. Hence, the particle is always accelerated by the electric field. As the energy of the particle increases, the radius of the circular path increases.
Time taken for a particle for one complete revolution = T
T =
Where is the cyclotron frequency
Then,
The above expression is the expression for cyclotron frequency.
The oscillator applies an ac voltage across the Ds and this voltage must have a frequency equalto that of cyclotron frequency.
Question 27 ( 3.0 marks)
Three light rays red (R), green (G) and blue (B) are incident on a right angled prism ‘abc’ at face
‘ab’. The refractive indices of the material of the prism for red, green and blue wavelengths are1.39, 1.44 and 1.47 respectively. Out of the three which colour ray will emerge out of face ‘ac’?
Justify your answer. Trace the path of these rays after passing through face ‘ab’.
The three light rays will go through ‘ab’ as the three are perpendicular to ‘ab’. However, whenthey will hit ‘ac’, they will refract with an angle of incidence of 45°.
Refractive indices for three light rays are given.
Red ( R) = 1.39
Green (G) = 1.44
Blue ( B) = 1.47
Total internal reflection takes place if the angle of incidence is such that
The refractive indices are from air to prism. To convert them from prism to air, we take their
Power consumed in both the coils is the same as even if the voltage increases or current
increases, their product at any instant remains the same.
Question 29 ( 5.0 marks)
(i) Draw a circuit diagram to study the input and output characteristics of an n-p-n transistor inits common emitter configuration. Draw the typical input and output characteristics.
(ii) Explain, with the help of a circuit diagram, the working of n-p-n transistor as a common
emitter amplifier.
OR
How is a zener diode fabricated so as to make it a special purpose diode? Draw I-Vcharacteristics of zener diode and explain the significance of breakdown voltage.
Explain briefly, with the help of a circuit diagram, how a p-n junction diode works as a half waverectifier.
Zener is fabricated such that both the p-type and the n-type are highly doped. This makes the
depletion region thin. When an electric field is applied, a high electric field appears across the
thin depletion region. When the electric field becomes very high, it knocks off electrons from thehost atoms to create a large number of electrons. This results in a large value of current inside the
circuit.
Zener has a sharp breakdown voltage and this property of zener is used for voltage regulation.
An ac current has a positive half cycle and a negative half cycle. A pn junction allows current to
pass only in one direction and that is when it is forward biased.
When a positive half-cycle occurs, the p-side has a lower potential. Therefore, the diode is nowforward biased and therefore conducts and this positive cycle is available for the load.
When a negative half cycle occurs, the n-side has a higher potential than the p-side. Hence, the
diode is now reverse biased and thus, does not conduct. As a result, this positive half cycle also
does not conduct. Therefore, it does not appear at the load and is cut-off.
We obtain a waveform, which has only positive half cycles and therefore it is called half-wave
rectifier.
Question 30 ( 5.0 marks)
Trace the rays of light showing the formation of an image due to a point object placed on the axisof a spherical surface separating the two media of refractive indices n1 and n2. Establish the
relation between the distances of the object, the image and the radius of curvature from the
central point of the spherical surface.
Hence derive the expression of the lens maker’s formula.
OR
Draw the labelled ray diagram for the formation of image by a compound microscope.
Derive the expression for the total magnification of a compound microscope. Explain why boththe objective and the eyepiece of a compound microscope must have short focal lengths.