P H Y S IC S TARGET : JEE (ADVANCED) 2016
O
Course : VIJETA & VIJAY (ADP & ADR)
Date : 07-04-2016
DPP DAILY PRACTICE PROBLEMS
NO. 01 This DPP is to be discussed (09-04-2016) CT-1 to be discussed (12-04-2016)
DPP No. # 01 Total Total Marks : 156 Single choice Objective (–1 negative marking) Q. 1 to 18 Multiple choice objective (–1 negative marking) Q. 19 to 29 Single Digit Subjective Questions (no negative marking) Q.30 to Q.34 Double Digits Subjective Questions (no negative marking) Q.35 to Q.36 Comprehension (–1 negative marking) Q.37 to 43 Match Listing (–1 negative marking) Q.44 to Q.46 1.
min. [54, 45] [44, 33] [20, 12½] [08, 05] [21, 17½] [09, 09]
The radius of a spherical planet having uniformly distributed mass is R. A satellite revolves around it in a circle of radius 'r' with angular speed . The acceleration due to gravity on planet’s surface will be (A)
2.
Max. Time : 122 (3 marks 2½ min.) (4 marks, 3 min.) (4 marks 2½ min.) (4 marks 2½ min.) (3 marks 2½ min.) (3 marks, 3 min.)
r 3 R
(B)
r 2 3 R
(C)
r 3 2 R2
(D)
r 2 2 R
The lens shown is equiconvex having refractive Index. 1.5. In the situation shown the final image of object coincides with the object. The region between lens and mirror is now filled with a liquid of refractive Index 2. Then find the separation between O & image formed by convex mirror. f = 20 cm
O 30 cm
(A) 33 cm 3.
(B) 66 cm
20 cm
(C) 16 cm
(D) 32 cm
A thin converging lens L1 forms a real image of an object located far away from the lens as shown in the figure. The image is located a distance 4 and has height 'h'. A diverging lens of focal length is placed 2 from lens L 1. Another converging lens of focal length 2 is placed 3 from lens L1. The height of final image thus formed is (Both diverging and converging lenses are placed at right side of L1 -
(A) h
(B)
h 2
(C) 4h
(D) 2h
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PAGE NO.-1
4.
A point object P is moving towards left with speed 5 mm/sec parallel to optical axis of a concave mirror of focal length f = 20 cm. The vertical seperation between object and optical axis is 1 cm. Find velocity of image of object in vector form when foot of perpendicular from object on the optical axis is at a distance 30 cm from pole.
(A) Vi 20iˆ 4 ˆj mm/sec (C) Vi 20iˆ ˆj mm/sec
(B) Vi 20iˆ ˆj mm/sec (D) Vi 20iˆ mm/sec
5.
Monochromatic light rays parallel to x-axis strike a convex lens AB. If the lens oscillates such that AB tilts upto a small angle (in radian) on either side of yaxis, then find the distance between extreme positions of oscillating image (f = focal length of the lens) : (A) 2(sec – 1) (B) f sec2 (C) (sec – 1) (D) the image will not move
6.
Two point charges having charge +Q, –q and mass M, m respectively are separated by a distance L. They are released from rest in a uniform electric field E. The electric field is parallel to line joining both the charges and is directed from negative to positive charge. For the separation between the particles to 1 remain constant, the value of L is (K = ) 4 0 (A)
7.
(M m) KQq E(qM Qm)
(M m) KQq E(qm QM)
(B)
At distance ' r ' from a point charge, the ratio
(C)
mM KQq E(qM Qm)
(D)
mM KQq E(QM qm)
U (where ' U ' is energy density and ' V ' is potential) is best V2
represented by : (A)
8.
(C)
(D)
A cylindrical portion of radius 'r' is removed from a solid sphere of radius R and uniform volume charge density in such a way that the axis of the hollow cylinder coincides with one of the diameters of the sphere. ('r' is negligible compared to R). Then the electric field intensity at point A is (A)
9.
(B)
rˆ i 3 0
(B)
rˆ i 3 0
(C)
rˆ i 6 0
(D)
A
r
j R i
rˆ i 6 0
A meteorite approaching a planet of mass M (in the straight line passing through the centre of the planet) collides with an automatic space station orbiting the planet in a circular trajectory of radius R. The mass of the station is ten times as large as the mass of the meteorite. As a result of the collision, the meteorite sticks with the station which goes over to a new orbit with the minimum distance R/2 from the planet. Speed of the meteorite just before it collides with the space station is : . (A)
58GM R
(B)
38GM R
(C)
28GM R
(D)
18GM R
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10.
Two converging lenses have focal length f1 and f2 (f1 >f2). The optical axis of the two lenses coincide. This lens system is used to from an image of real object. It is observed that final magnification of the image does not depend on the distance x. Whole arrangement is shown in figure. Final magnification is :
(A)
f1 f2
(B)
f2 f1
(C)
f1 f1 f2
(D)
f2 f1 f2
11.
In the figure shown, an infinitely long wire of uniform linear charge density is kept perpendicular to the plane of figure such that it extends upto infinity on both sides of the paper. Find the electrostatic force on a semicircular ring kept such that its geometrical axis coincides with the wire. The semicircular ring has a uniform linear charge density . (A) (B) (C) (D) 0R 40 20 0
12.
A satellite with mass 2000 kg and angular momentum magnitude 2 × 1012 kg.m 2/s is moving in an elliptical orbit around a planet. The rate at which area is being swept out by the satellite around the planet, is equal to (A) 1 × 109 m 2/s (B) 5 × 109 m 2/s (C) 5 × 108 m 2/s (D) 4 × 1015 m 2/s
13.
A concave mirror of radius of curvature 40 cm is filled with water (n = 4/3) upto a height of 12 cm. A point object O is kept on the principal axis of the mirror at height 13.5 cm from the water surface. The final image formed after refraction at water surface, reflection at mirror and again refraction at water surface in succession is situated at.
(A) 36 cm above the water surface (C) 20 cm above the water surface
(B) 24 cm above the water surface (D) 12 cm above the water surface
14.
Consider a spherical planet rotating about its axis. The velocity of a point at equator is v. The angular velocity of this planet is such that it makes apparent value of ‘g’ at the equator half of value of ‘g’ at the pole. The escape speed for a polar particle on the planet expressed as multiple of v is : (A) v (B) 2v (C) 3v (D) 4v
15.
The figure shows two equal, positive charges, each of magnitude 50 C, fixed at points (3, 0) m and (–3, 0)m respectively. A charge –50C, moving along negative y–axis has a kinetic energy of 4J at the instant it crosses point (0,4)m. Determine the position of this charge where the direction of its motion reverses for the first time after crossing this point (neglect gravity).
(A) 0m, 7 2m (C) (0, 5 2)
(D) 0m, 4 2 m (B) 0, 6 2m
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16.
17.
Orbital velocity of a satellite in its orbit (around earth) of radius 'r' is 'v'. It collides with another body in its orbit and comes to rest just after the collision. Taking the radius of earth as R, the speed with which it will fall on the surface of earth will be : v r r r (A) v ( 1) (B) v 2( 1) (C) (D) v 2( 1) R R R r 2( 1) R Three charges q, q and -2q are fixed on the vertices of an non conducting equilateral triangular plate of edge length 'a'. This plate is in equilibrium between two very large plates having surface charge density 1 & 2 respectively. The period of small angular oscillation about an axis passing through its centroid and perpendicular to plane is : (Moment of inertia of the system about this axis is ) 0 I 0 I (A) 2 (B) 2 qa 1 – 2 2qa 1 – 2 (C) 2
18.
19*.
20 I 3qa 1 – 2
(D) 2
0 I qa 1 – 2
A uniformly charged non conducting sphere (in volume) of radius R and total charge Q is fixed on a non-conducting platform. A very small bob having negative charge –q and mass m is hung from a fixed point through a non-conducing and inextensible string of length 2R as shown in the figure. The whole system is placed in a gravity free space. The bob is displaced by a very small angle from the vertical, then find time required to reach from point A to O. (Angular displacement of the bob is so small that it can be assumed, the distance between the bob and the sphere is always nearly equal to R) (A) 2
4 0 R 3 m 3Qq
(B)
4 0 R 3 m 2 3Qq
(C) 2
8 0 R 3 m 3Qq
(D)
8 0 R 3 m 2 3Qq
2R
O
A
R
A person is looking at the flat surface of a transparent hemisphere. Half of the flat surface is coloured black and half of curved surface is coloured in six equal strips as shown in the figure. Then select correct alternative/s (nR = 1.412, nO = 1.413, nY = 1.414, n G = 1.415, nB= 1.416, nV = 1.417) (where alphabates has usual meaning)
(A) The person can see green orange and red (B) The person can see only yellow, indigo and blue (C) The ray coming from green, red and orange strips will be totally reflected (D) The ray coming from yellow, indigo and blue strips will be totally reflected
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20.
When a short dipole is placed inside a cavity in a solid neutral conducting body : (A) No charges are induced on the inner surface of cavity (B) No charges are induced on the outer surface of conducting body (C) Everywhere outside the body electric field due to dipole is zero (D) Everywhere outside the body net electric field is zero
21.
An uncharged conducting sphere of radius R is placed near a uniformly charged ring of radius R. Total charge on ring is Q. The centre of sphere lies on the axis of ring and distance of centre of sphere from centre of ring is R.
R KQ (A) Potential at centre of ring is R KQ (B) Potential at centre of ring is 2R (C) Potential at centre of ring due to conducting sphere is zero KQ (D) Potential at centre of conducting sphere is 2R 22.
Three point masses A,B,C each of mass m are moving on the same circular path and are always equidistant from each other. The radius of circle is R and the speed of each mass is same and equal to V. The only force acting on each mass is the graviational force because of the other two masses. Choose the correct statement. (A) power of the graviational force by A on B is non-zero (B) power of the graviational force by A on B is zero 3mV 3 (C) magnitude of power of the total graviational force on A in the frame of B is 2R (D) the ratio of magnitude of relative velocity of A with respect B and A with respect to C is 1 : 1
23.
A luminous point object is placed at O, whose image is formed at as shown in figure. Line AB is the optical axis. Which of the following statement is/are correct ?
(A) If a lens is used to obtain the image, then it must be a converging lens and its optical centre will be the intersection point of line AB and O. (B) If a lens is used to obtain the image, then it must be a diverging lens and its optical centre will be the intersection point of line AB and O. (C) If a mirror is used to obtain the image then the mirror must be concave and object and image subtend equal angles at the pole of the mirror. (D) is a real Image.
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24.
A solid spherical planet of mass 2m and radius 'R' has a very small tunnel along its diameter. A small cosmic particle of mass m is at a distance 2R from the centre of the planet as shown. Both are initially at rest, and due to gravitational attraction, both start moving toward each other. After some time, the cosmic particle passes through the centre of the planet. (Assume the planet and the cosmic particle are isolated from other planets)
4R 3 (B) Acceleration of the cosmic particle at that instant is zero
(A) Displacement of the cosmic particle till that instant is
(C) velocity of the cosmic particle at that instant is
8Gm 3R
(D) Total work done by the gravitational force on both the particle is 25.
2Gm2 R
In the figure shown A & B are two charged particles having charges q and – q respectively are placed on a non-conducting fixed horizontal smooth plane. B is fixed and A is attached to a non conducting massless spring of spring constant 'k'. The other end of the spring is fixed. Mass of A is m, A and B are in equilibrium when the distance between them is 'r'. Choose the correct options
m
(A) time period of small oscillation of block A about its mean position is 2 k
q2 2 0 r3 m
(B) time period of small oscillation of block A about its mean position is 2 k
q2 2 0 r3
q2 (C) to perform SHM, K must be greater than . 2 r 3 0 2q2 (D) to perform SHM, K must be greater than r 3 0
26.
x where 4 n 0 = 1. The medium is bounded by the planes x = 0, x = 1 & y = 0. If the ray enters at the origin at an angle 30º with x–axis.
A light ray enters into a medium whose refractive index varies along the x-axis as n(x ) n0 1
(A) equation of trajectory of the light ray is y = [ 3 x 3 ] (B) equation of trajectory of the light ray is y = 2[ 3 x 3 ] (C) the coordinates of the point at which light ray comes out from the medium is [1, 2(2 – 3 )] (D) the coordinates of the point at which light ray comes out from the medium is [0, 2(2 – 3 )] Corporate Office : CG Tower, A-46 & 52, IPIA, Near City Mall, Jhalawar Road, Kota (Raj.) - 324005 Website: www.resonance.ac.in | E-mail :
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PAGE NO.-6
27.
Two infinite, parallel, non–conducting thin sheets carry equal positive charge density . One is placed in the yz plane and the other at x = a. Take potential V = 0 at x = 0. Choose the correct statements (A) For 0 x a, potential V = 0. (B) For x a, potential V = (x a) 0 (C) For x a, potential V = (D) For x 0 potential V =
28.
x 0
In the figure shown there is a hollow hemisphere of radius 'R'. It has a uniform mass distribution having total mass 'm'. The gravitational potential at points A, D and B are VA, VD and VB respectively. Distance of D and B from centre C are R/2 and 2R respectively. The points C, D and B are lying on radial line of the hollow hemisphere.
(A) VA = – 29.
(x a) 0
Gm , R
(B) VD = –
Gm R
(C) VB = –
Gm 2R
(D) VA = VD < VB
In a certain universe, the gravity is a conservative force but not necessarily an inverse square law force. In that universe, there exists a single point like mass 'm' that is influenced only by gravity. As a result of a gravitational force, the mass orbits the fixed source (point O) in a circle, so that the source point is on the circle's rim. Neglecting the singular point, select that correct alternative/s. ('r' is the distance of 'm' from O) V0
P OP=2R
r
O
(A) Velocity of the point mass as function of r is given by
4R2 V0
(r 0) r2 (B) Force experienced by point mass depends on intial speed V0 of point mass. (C) Force experienced by point mass will be inversly proportnal to fifth power of its distance from O. (D) Position vector of particle with respect to centre of circle sweeps out equal area in equal interval of time. 30.
Two parallel beams of light pass through an isosceles prism of refractive index 1.4 as shown in the figure. The angle between the two emergent rays is 18Xº calculate X.[sin350 = 0.57, sin-1(0.798) = 530]
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31.
A cavity of radius 'r' is present inside a fixed solid dielectric sphere of radius R, having a volume charge density of ''. The distance between the centres of the sphere and the cavity is 'a'. An electron is released inside the cavity at an angle = 45 0 as shown. The electron (of mass 'm' and charge '–e') will take P 2mr0 ea
1/ 2
time to touch the sphere again. Neglect gravity. Find the value of P :
32.
A uniform thin rod of mass m and length R is placed normally on surface of earth as shown. The mass of GMm earth is M and its radius is R. If the magnitude of gravitational force exerted by earth on the rod is , 12R 2 then ‘’ is
33.
A planet is made of two materials of density '1' and '2' as shown in figure.
Acceleration due to gravity at surface of planet is same as that at depth ‘R’. The ratio
1 x is equal to . 2 3
Find the value of 'x'. 34.
Figure shows an irregular block of material of refractive index 2 . A ray of light strikes the face AB as shown in figure. After refraction it is incident on a spherical surface CD of radius of curvature 0.4 m, (with centre lying on the line PQ) and enter a medium of refractive index 1.514 to meet PQ at E. Find the distance OE. in nearest interger in meters (point M is very near to line PQ) M
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35.
Two persons A and B wear glasses of optical powers (in air) P1 = + 2 D and P2 = + 1D respectively. The glasses have refractive index 1.5. Now they jump into a swimming pool and look at each other. B appears to be present at distance 2m (from A) to A. A appears to be present at distance X 1m (from B) to B. The refractive index of water in the swimming pool, in the form and find X. 10
36.
The final image of the object O shown in the figure is formed at point 20 cm below a thin equi-concave lens, which is at a depth of 65 cm from principal axis. From the given geometry, calculate the radius of curvature in cm of lens kept at "A". (Refractive index of equi-convex lens is 1.5 and placed in air).
COMPREHENSION -1 The curve of angle of incidence versus angle of deviation shown has been plotted for prism.
37.
The value of refractive index of the prism used is (A)
38.
3
(B)
(C)
2
The value of angle i1 in degrees is (A) 40° (B) 60°
3/ 2
(C) 70°
(D) 2 / 3
(D) 90°
COMPREHENSION -2 There are two non-conducting spheres having uniform volume charge densities and –. Both spheres have equal radius R. The spheres are now laid down such that they overlap as shown in the figure.
39.
The electric field E in the overlapped region is (A) non uniform
40.
(B) zero
(C)
d 3 0
(D)
R 3 0
The potential difference V between the centers of the two spheres for d = R is : 2 2 2 2 (A) d (B) d (C) zero (D) d 3 0 0 0
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COMPREHENSION -3 A charge 'q' is divided into three equal parts and placed symmetrically on a circle of radius 'r'. The same charge is divided into four equal parts and placed symmetrically on the same circle. The electric field intensities at the centre of the circle in two situations are zero. 41.
The ratio of electric potentials at the centre in the two situations is 2 1 4 (A) (B) (C) 1 3 3
(D)
16 9
42.
The potential energy of the system in first situation where the charge is divided into three equal parts is 1 q2 1 q2 1 q2 1 q2 (A) (B) (C) (D) 4o r 36 o r 12 o r 12 3 o r
43.
If a charge is removed from one location in both the situations, the ratio of magnitudes of the electric field intensities at the centre is 1 1 2 4 (A) (B) (C) (D) 2 1 3 3
44.
Match the proper entries from column-2 to column-1 using the codes given below 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 0º and 180º. Here n represents refractive index of medium. Column–I Column–II (P)
(1) deviation in the light ray is greater than 90º
(Q)
(2) deviation in the light ray is less than 90º
(R)
(3) deviation in the light ray is equal to 90°
(S)
(4) Speed of finally reflected or refracted light is
same as speed of incident light. (A) (B) (C) (D)
(P) 4 1 3 2
(Q) 2 2 1 4
(R) 1 4 4 1
(S) 3 2 2 3
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45.
In each situation of column-I, some charge distributions are given with all details explained. In column -II The electrostatic potential energy and its nature is given situation in column -II. Match the proper entries from column-2 to column-1 using the codes given below the columns, Column-I Column-II (P) A thin shell of radius 'a' and having a charge – Q uniformly distributed
(1)
1 Q2 in magnitude 8 0 a
(2)
3 Q2 in magnitude 20 0 a
(3)
27 Q2 in magnitude 80 0 a
over its surface as shown
(Q) A thin shell of radius
5 a and having 2
a charge – Q uniformly distributed over its surface and a point charge – Q placed at its centre as shown.
(R) A solid sphere of radius 'a' and having a charge – Q uniformly distributed throughout its volume as shown.
(S) A solid sphere of radius 'a' and having a charge – Q uniformly distributed throughout its volume. The solid sphere is surrounded by a concentric thin uniformly charged spherical shell of radius 2a and carrying charge –Q as shown
(A) (B) (C) (D)
(P) 1 4 1 2
(Q) 2 1 2 4
(R) 4 2 3 3
(4) Positive in sign
(S) 3 3 4 1
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46.
A conducting sphere A of radius 'a', with charge Q is placed concentrically inside a conducting shell B of radius 'b'. B is earthed, C is the common centre of A and B. If P is the point between shells A and B at distance 'r' from center C then Match the proper entries from column-2 to column-1 using the codes given 1 below the columns, (use : a = 1m, b = 3m, r = 2 m and K = ) 40
b B
A
a C
Column - I (P)
Electric field at point P is
(Q)
Electric potential at point P is (v = 0)
Column - II 2KQ (1) 3 (2) zero
(R)
Electric potential difference between A and B is
(3)
(S)
Electric field outside the shell B at distance
(A) (B) (C) (D)
5 m from centre C is (P) (Q) (R) 3 1 2 1 2 3 2 3 4 3 4 1
KQ 4 KQ (4) 6
(S) 4 4 1 2
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PAGE NO.-12
