(a) The final charge on initially neutral conducting sphere is −Q
3.
(b) The decrease in electric potential energy of sphere of radius R is 35
72 kQ2
R .
(c) The decrease in electric potential energy of sphere of radius R is 37
72 kQ2
R .
(d) The final electric potential on sphere of radius 3R will be − kQ
R 6 .
8. In the given circuit, R1R4 = R2R3.
Then choose the correct statement(s).
(a) If positions of battery and galvanometer are i n t e r c h a n g e d , t h e n galvanometer will still show zero deflection.
(b) Rate of heat dissipation through R1 will change if position of battery and galvanometer are interchanged.
(c) If emf e is doubled, still no deflection is shown by galvanometer.
(d) If galvanometer is not ideal, it will show deflection if emf is doubled.
9. A lens made from a material of refractive index 1.5 behaves as a converging lens in air. When placed in liquid of refractive index 8/5, it will
(a) still behave as a converging lens (b) behave as a diverging lens (c) have its focal length increased (d) have its focal length decreased
10. Figure shows a square loop of side 10 cm in the x-y plane with its centre at the origin. An infinite wire is at z = 12 cm above y-axis.
Which of the following statements are correct ? (a) Resultant magnetic force on loop due to infinite
wire is 6 × 10–3 N.
(b) magnetic force on wire segment AB due to infinite wire is in positive x-direction.
(c) magnetic force on wire segment CD due to infinite wire is in negative x-direction.
(d) Torque on loop due to magnetic force is 7.2 × 10–5 N m.
11. The switches in figures (a) and (b) are closed at t = 0.
Then
(a) The charge on C just after t = 0 is eC.
(b) The charge on C long after t = 0 is eC.
(c) The current in L just after t = 0 is e/R.
(d) The current in L long after t = 0 is e/R.
12. A microammeter has a resistance of 100 Ω and a full scale range of 50 mA. It can be used as a voltmeter or as a higher range ammeter provided a resistance is added to it. Pick the correct range and resistance combinations(s).
(a) 50 V range with 10 kΩ resistance in series.
(b) 10 V range with 200 kΩ resistance in series.
(c) 5 mA range with 1 Ω resistance in parallel.
(d) 10 mA range with 1 Ω resistance in parallel.
Section-3
comprehension Type (only one option correct) This section contains 1 paragraph, describing theory, experiments, data etc. Two questions relate to the paragraph.
Each question has only one correct answer among the four given options (a), (b), (c) and (d).
Paragraph for Question Nos. 13 and 14 Uniform electric and magnetic fields with strength E and induction B, respectively, are along y-axis as shown in figure. A particle with specific charge q/m leaves the origin O in the direction of x-axis with an initial non-relativistic velocity v0.
13. The coordinate yn of the particle when it crosses the
14. The angle a between the particle’s velocity vector and velocity along y-axis at that moment is
(a) tan− Column-I and Column-II are given as options (a), (b), (c) and (d), out of which one is correct.
15. match the columns if deviation in the column II is the magnitude of total deviation (between incident ray and finally refracted or reflected ray) to lie between 0° and 180°. Here n represents refractive index of medium.
Column I Column II
P. 1. Deviation in the
light ray is greater than 90°
When S is opened, capacitor B will be disconnected from the battery while capacitor A will remain connected to the battery. In such a case, potential difference across A remains the same , V while the charge on B remains the same i.e., CV.
Since the space between the plates of the capacitors A and B is filled with a dielectric of dielectric constant k(=3), capacitance of each capacitor is kC.
U U U kC V CV
2. (2) When no matter was filled, it behaves like an air convergent lens of focal length 15 cm.
Let mm be the refractive index of the material to be filled. Initially there are two identical dipoles at right angles to each other, so resultant magnetic moment,
M0= M2+M2 = 2M
And when one magnet is taken away, the other will oscillate with period given by eqn (i), so dividing eqn (i) by (ii), From equations (ii) and (iii)
1
6. (7) Points B and D have same potential, similarly F and H have same potential. The equivalent circuit is shown in figure.
The equivalent resistance of network is 7R/12.
7. (a, b, d) : Finally, potential on all spheres will be equal.
i.e., kQ
Change in electric potential energy of sphere of radius R = Ui – Uf
Potential on sphere of radius 3R
= −
i.e. Wheatstone bridge condition is satisfied.
∴ No deflection in galvanometer.
Initially current through R1 is I1=R R1 2
+ e
Now current through R1 after interchanging I2=R R1 3
+ e Since current has changed,
∴ Rate of heat dissipation changes.
Since current through galvanometer is zero,
∴ It will always show zero deflection for any starts charging such that charge on C at any time t is given by
q=eC
(
1−e−t CR/)
.∴ Charge on C just after t = 0 is zero and long after t = 0 (t → ∞) is ε C.
As switch in figure (b) is closed, that grows a current such that current in L at any time t is
I = Re
(
1−e−tR L/)
. ammeter. Let S be the low resistance.∴ SG
Option (c) is correct.
In order to change ammeter into a voltmeter, a high resistance is connected in series with the ammeter.
Let the high resistance be R.
∴ I R G Vg( + )= Option (b) is correct.
13. (a) : Particle’s acceleration is in y-direction, dv
dt qE
m
y = = constant
The motion of the particle is equivalent to circular motion in x–z plane with uniform acceleration in y-direction.
Hence, v v v02= x2+ = constantz2
The magnetic force cannot change the magnitude of v0 .
The y-component of velocity, v qEy= mt The y-coordinate at time t, y qE
mt
= 12 2
The time period of circular motion in x–z plane,
T m
= 2πqB
The particle crosses y-axis after n rotations, then
t nT mn
1. A person sitting in a satellite of Earth feels weightlessness but a person standing on Moon has weight though Moon is also a satellite of Earth. Why?
2. A wire of length L and cross-sectional area A is made of material of Young’s modulus Y. What is the work done in stretching the wire by an amount x?
3. The velocity of water in a river is less on the bank and large in the middle; why?
4. A blackened platinum wire, when gradually heated, first appears dull red, then blue and finally white.
Explain why.
5. Why iron rims are heated red hot before being put on the cart wheels?
6. When the tension in a metal wire is T1, its length is l1. When the tension is T2, its length is l2. Find the natural length of wire.
7. The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble.
What is the ratio between the volume of the first and the second bubble?
8. A simple pendulum has a time period T1 on the earth’s surface, and T2 when taken to a height R above the earth’s surface, where R is the radius of the earth. What will be the value of T2/T1?
Series 3
An astronaut on the Moon measures the acceleration OR due to gravity to be 1.7 m s–2. He knows that the radius of the Moon is about 0.27 times that of the Earth. What is his estimate of the ratio of the mass of the Earth to that of the Moon? (Take, acceleration due to gravity on the Earth’s surface as 9.8 m s–2) 9. A cable is replaced by another of the same length
and material but of twice the diameter. (a) How does this affect its elongation under a given load?
(b) How many times will be the maximum load it can now support without exceeding the elastic limit?
10. Explain why:
(i) A balloon filled with helium does not rise in air indefinitely but halts after a certain height (Neglect winds).
(ii) The force required by a man to raise his limbs immersed in water is smaller than the force for the same movement in air.
11. If an isotropic solid has coefficients of linear expansion, ax, ay and az for three mutually perpendicular directions in the solid, what is the coefficient of volume expansion for the solid?
GENERAL INSTRUCTIONS (i) All questions are compulsory.
(ii) Q. no. 1 to 5 are very short answer questions and carry 1 mark each.
(iii) Q. no. 6 to 10 are short answer questions and carry 2 marks each.
(iv) Q. no. 11 to 17 are also short answer questions and carry 3 marks each.
(v) Q. no. 18 is a value based question and carries 4 marks.
(vi) Q. no. 19 and 20 are long answer questions and carry 5 marks each.
(vii) Use log tables if necessary, use of calculators is not allowed.