1. Xtra Edge February 2012 - Career Point
1. Xtra Edge February 2012 - Career Point 1. Xtra Edge February 2012 - Career Point
(A) (C) λ 2πε0 λ 4πε 0 13 ln (B) 5 13 ln (D) 5 2λ 13 ln πε 0 3 λ 13 ln πε 0 3 6. A satellite is put in an orbit just above the earth atmosphere with a velocity 1 . 5 times the velocity for a circular orbit at that height. The initial velocity imparted is horizontal. What would be the maximum distance of satellite from earth when it is in the orbit- (A) 3R (B) 4R (C) 2 R (D) 5 R 7. The density of a uniform rod with cross section area A is ρ, its specific heat capacity is C and the coefficient of its linear expansion is α. Calculate the amount of heat that should be added in order to increase the length of the rod by ∆l. 2AρC∆l AρCα (A) (B) α ∆l AρC∆l ρC∆l (C) (D) α 2Aα 8. For the system shown each spring has a stiffness of 175 N/m. The mass of the pulleys may be neglected. The period of vertical oscillation of block – (mass of block is 28 kg) k k Block 28 kg fricationless surface π π (A) 2 s (B) π 2 s (C) s (D) 5 5 9. A uniform elastic rod of cross section area A, natural length L and young modulus Y is placed on a smooth horizontal surface. Now two horizontal force (of magnitude F and 3F) directed along the length of rod and in opposite direction act at two of its ends as shown. After the rod has acquired steady state (i.e. no further extension take place), the extension of the rod will be – Elastic rod F 3F 2F (A) L YA 4F (B) L YA F (C) L YA 3F (D) L 2YA 2 s This section contains 4 questions numbered 10 to 13, (Reason and Assertion type question). Each question contains Assertion (A) and Reason (R). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Mark your response in OMR sheet against the question number of that question. +3 marks will be given for each correct answer and – 1 mark for each wrong answer. The following questions given below consist of an "Assertion" (A) and "Reason" (R) Type questions. Use the following Key to choose the appropriate answer. (A) If both (A) and (R) are true, and (R) is the correct explanation of (A). (B) If both (A) and (R) are true but (R) is not the correct explanation of (A). (C) If (A) is true but (R) is false. (D) If (A) is false but (R) is true. 10. Assertion (A) : As the earth revolves around the sun it has an acceleration which is directed towards centre of the sun. Reason (R) : Angular momentum of the earth about the sun remains constant. 11. Assertion (A) : In electric circuits , wires carrying currents in opposite direction are often twisted together. Reason (R) : The magnetic field in the surrounding space of a twisted wire system in not precisely zero. 12. Assertion (A) : A metal ball is floating in mercury. Coefficient of volume expansion of metal is less than that of mercury. If temperature is increased, fraction of volume immersed of metal will increase. Reason (R) : Effect of heating on density of mercury will be more compared to that of metal. 13. Assertion (A) : Work done by static friction is always zero. Reason (R) : Static friction acts when there is no relative motion between two bodies in contact. This section contains 2 paragraphs; each has 3 multiple choice questions. (Questions 14 to 19) Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Mark your response in OMR sheet against the question number of that question. +4 marks will be given for each correct answer and – 1 mark for each wrong answer. Passage # 1 (Ques. 14 to 16) A conducting rod PQ of mass M rotates without friction on a horizontal plane about Ο on circular rails of diameter 'l'. The centre O and the periphery are connected by resistance R. The system is located in a uniform magnetic field perpendicular to the plane of the loop. At t = 0, PQ starts rotating clockwise with angular velocity ω0. Neglect the resistance of the rails and rod, as well as self inductance. XtraEdge for IIT-JEE 48 FEBRUARY 2012
R P ⊗ B O ω0 14. Magnitude of current as a function of time 2 Bω0l −αt (A) e 2R 2 Bω0l −2αt (B) e 16R 2 Bω0l −αt (C) e 8R 2 2 3B l Where α = 8RM 2 Bω0l −2αt (D) e 8R 15. Total charge flow through resistance till rod PQ stop rotating . ω0M ω0M (A) (B) 8B 3B ω0M ω0M (C) (D) 6B 9B 16. Heat generated in the circuit by t = ∞ M (A) 24 2 2 l ω0 M (B) 8 2 2 l ω0 M (C) 3 2 2 l ω0 M (D) 32 2 2 l ω0 Passage # 2 (Ques. 17 to 19) A cylindrical spool of radius R is rigidly attached to a pulley of radius 2R. The mass of the combination is m and the radius of gyration about the centroidal axis G is R. A constant horizontal force F is applied at one end of the tape. Assume rolling motion between the pulley and the ground. I is the moment of inertia about centroidal axis. 2R G R 17. The acceleration of point P on the tape relative to the ground is - F (A) 2m F (B) 5m F (C) 3m F (D) 4m 18. The length of the tape wound/unwound on the spool in time t is - Ft (A) 10 m 2 Ft (B) 5m 2 Ft (C) 4m 2 Ft (D) 2m 2 19. The linear acceleration of centre G is - 2 2FR (A) I 2 2FR (B) 2 I + mR 2 2FR (C) 2 I + 2mR 2 2FR (D) 2 I + 4mR P Q F This section contains 3 questions (Questions 20 to 22). Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (P, Q, R, S) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example. If the correct matches are A-P, A-S, B-Q, B-R, C-P, C-Q and D-S, then the correctly bubbled 4 × 4 matrix should be as follows : P Q R S A P Q R S B P Q R S C P Q R S D P Q R S Mark your response in OMR sheet against the question number of that question in section-II. + 6 marks will be given for complete correct answer and No Negative marks for wrong answer. However, 1 mark will be given for a correctly marked answer in any row. 20. A charged particle passes through a region that could have electric field only or magnetic field only or both electric and magnetic field or none of the fields. Match the possibilities Column-I (A) Kinetic energy of the particle remain constant. (B) Acceleration of the particle is zero (C) Kinetic energy of the particle changes and it also suffers deflection (D) Kinetic energy of the particle changes but it suffers no deflection Column-II (P) Under special condition this is possible when both electric and magnetic fields are present (Q) The region has electric field (R) The region has magnetic field only (S) The region contains no field 21. Match the column : Column-I Phenomena on which machine work (A) Electromagnetic induction (B) Light of suitable frequency falling on a material result in emissions of electrons from the material (C) Change of orientation of a coil in a magnetic field results in e.m.f. across the coil (D) Mutual induction Column-II Machine or instrument (P) Photocell (Q) DC motor (R) AC generator (S) Transformer XtraEdge for IIT-JEE 49 FEBRUARY 2012
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R<br />
P<br />
⊗ B<br />
O ω0<br />
14. Magnitude of current as a function of time<br />
2<br />
Bω0l −αt<br />
(A) e<br />
2R<br />
2<br />
Bω0l −2αt<br />
(B) e<br />
16R<br />
2<br />
Bω0l −αt<br />
(C) e<br />
8R<br />
2 2<br />
3B<br />
l<br />
Where α =<br />
8RM<br />
2<br />
Bω0l −2αt<br />
(D) e<br />
8R<br />
15. Total charge flow through resistance till rod PQ stop<br />
rotating .<br />
ω0M<br />
ω0M<br />
(A) (B)<br />
8B<br />
3B<br />
ω0M<br />
ω0M<br />
(C) (D)<br />
6B<br />
9B<br />
16. Heat generated in the circuit by t = ∞<br />
M<br />
(A)<br />
24<br />
2 2<br />
l ω0<br />
M<br />
(B)<br />
8<br />
2 2<br />
l ω0<br />
M<br />
(C)<br />
3<br />
2 2<br />
l ω0<br />
M<br />
(D)<br />
32<br />
2 2<br />
l ω0<br />
Passage # 2 (Ques. 17 to 19)<br />
A cylindrical spool of radius R is rigidly attached to a<br />
pulley of radius 2R. The mass of the combination is<br />
m and the radius of gyration about the centroidal axis<br />
G is R. A constant horizontal force F is applied at<br />
one end of the tape. Assume rolling motion between<br />
the pulley and the ground. I is the moment of inertia<br />
about centroidal axis.<br />
2R<br />
G R<br />
17. The acceleration of point P on the tape relative to the<br />
ground is -<br />
F<br />
(A)<br />
2m<br />
F<br />
(B)<br />
5m<br />
F<br />
(C)<br />
3m<br />
F<br />
(D)<br />
4m<br />
18. The length of the tape wound/unwound on the spool<br />
in time t is -<br />
Ft<br />
(A)<br />
10 m<br />
2<br />
Ft<br />
(B)<br />
5m<br />
2<br />
Ft<br />
(C)<br />
4m<br />
2<br />
Ft<br />
(D)<br />
2m<br />
2<br />
19. The linear acceleration of centre G is -<br />
2<br />
2FR<br />
(A)<br />
I<br />
2<br />
2FR<br />
(B)<br />
2<br />
I + mR<br />
2<br />
2FR<br />
(C)<br />
2<br />
I + 2mR<br />
2<br />
2FR<br />
(D)<br />
2<br />
I + 4mR<br />
P<br />
Q<br />
F<br />
This section contains 3 questions (Questions 20 to 22).<br />
Each question contains statements given in two columns<br />
which have to be matched. Statements (A, B, C, D) in<br />
Column I have to be matched with statements (P, Q, R, S)<br />
in Column II. The answers to these questions have to be<br />
appropriately bubbled as illustrated in the following<br />
example. If the correct matches are A-P, A-S, B-Q, B-R,<br />
C-P, C-Q and D-S, then the correctly bubbled 4 × 4<br />
matrix should be as follows :<br />
P Q R S<br />
A P Q R S<br />
B P Q R S<br />
C P Q R S<br />
D P Q R S<br />
Mark your response in OMR sheet against the question<br />
number of that question in section-II. + 6 marks will be<br />
given for complete correct answer and No Negative<br />
marks for wrong answer. However, 1 mark will be<br />
given for a correctly marked answer in any row.<br />
20. A charged particle passes through a region that could<br />
have electric field only or magnetic field only or both<br />
electric and magnetic field or none of the fields.<br />
Match the possibilities<br />
Column-I<br />
(A) Kinetic energy of the particle remain constant.<br />
(B) Acceleration of the particle is zero<br />
(C) Kinetic energy of the particle changes and it also<br />
suffers deflection<br />
(D) Kinetic energy of the particle changes but it<br />
suffers no deflection<br />
Column-II<br />
(P) Under special condition this is possible when<br />
both electric and magnetic fields are present<br />
(Q) The region has electric field<br />
(R) The region has magnetic field only<br />
(S) The region contains no field<br />
2<strong>1.</strong> Match the column :<br />
Column-I<br />
Phenomena on which machine work<br />
(A) Electromagnetic induction<br />
(B) Light of suitable frequency falling on a material<br />
result in emissions of electrons from the material<br />
(C) Change of orientation of a coil in a magnetic<br />
field results in e.m.f. across the coil<br />
(D) Mutual induction<br />
Column-II<br />
Machine or instrument<br />
(P) Photocell<br />
(Q) DC motor<br />
(R) AC generator<br />
(S) Transformer<br />
<strong>Xtra</strong><strong>Edge</strong> for IIT-JEE 49 FEBRUARY <strong>2012</strong>
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