FIIJEE Solutions to IIJEE 00 Mains Paper ime: hours Physics Note: Question number 1 to 10 carries marks each and 11 to 0 carries marks each. 1. long wire of negligible thickness and mass per unit length λ is floating in a liquid such that the top surface of liquid dips by a distance y. If the length of base of vessel is a, find surface tension of the liquid. (y < < a) a a y ( cos θ) λ g λg cosθ λ g(a + y ) y 1/ λga y. θ. n ideal diatomic gas is enclosed in an insulated chamber at temperature 00K. he chamber is closed by a freely movable massless piston, whose initial height from the base is 1m. Now the gas is heated such that its temperature becomes 00 K at constant pressure. Find the new height of the piston from the base. If the gas is compressed to initial position such that no exchange of heat takes place, find the final temperature of the gas. tmosphere 1m Process 1 is isobaric 1 00 K, 00 K V constant 1 h h m 00 00 Process is adiabatic V γ 1 constant, 7 1 5 7 1 5 00 ( ) 5 1 00 K.. In Searle s apparatus diameter of the wire was measured 0.05 cm by screw gauge of least count 0.001 cm. he length of wire was measured 110 cm by meter scale of least count 0.1 cm. n external load of 50 N was applied. he extension in length of wire was measured 0.15 cm by micrometer of least count 0.001 cm. Find the maximum possible error in measurement of young s modulus. F/ πd F Y ( )/ πd ( ) Maximum possible relative error FIIJEE td. ICES House, Sarvapriya Vihar (Near Hauz Khas Bus erm.), New Delhi - 16, Ph : 686 518, 696566, 685 10, 651599 Fax : 6519
II-JEE 00-M- ( ) Y D 0.1 0.001 0.001 + + + + Y D 110 0.050 0.15 Percentage error Y 1 100 + + Y 11 5 0.8 + + 0.09.89 %.. wo infinitely large sheets having charge densities σ 1 and σ respectively (σ 1 > σ ) are placed near each other separated by distance d. charge Q is placed in between two plates such that there is no effect on charge distribution on plates. Now this charge is moved at an angle of 5 0 with the horizontal towards plate having charge density σ by distance a (a < d). Find the work done by electric field in the process. σ 1 a B 5 0 d σ ( σ1 σ) E ε 0 work done by electric field, W q E. d a q( σ1 σ)a E q ε 0 5. n α -particle and a proton are accelerated from rest through same potential difference and both enter into a uniform perpendicular magnetic field. Find the ratio of their radii of curvature. r qvm qb r m q r m q α p α p p α e 1 e :1 6. small ball of radius r is falling in a viscous liquid under gravity. Find the dependency of rate of heat produced in terms of radius r after the drop attains terminal velocity. ate of heat produced F.v 6πη rv.v dq 6 πη dt r.v v ( ) σ ρ r g/ η 9 dq r 5 dt 7. syringe of diameter D 8 mm and having a nozzle of diameter d mm is placed horizontally at a height of 1.5 m as shown in the figure. n incompressible and non-viscous liquid is filled in syringe and the piston is moved at speed of 0.5 m/s. Find the range of liquid jet on the ground. h1.5 m V0.5 m/s FIIJEE td. ICES House, Sarvapriya Vihar (Near Hauz Khas Bus erm.), New Delhi - 16, Ph : 686 518, 696566, 685 10, 651599 Fax : 6519
II-JEE 00-M- V Constant D V d v D 8 v V 0.5 d 16 0.5 m / s h 1.5 1 x v m g 10 8. light ray is incident on an irregular shaped slab of refractive index at an angle of 5 with the normal on the incline face as shown in the figure. he ray finally emerges from the curved surface in the medium of the refractive index µ 1.51 and passes through point E. If the radius of curved surface is equal to 0. m, find the distance E correct upto two decimal places. P B µ 1 1 µ 5 0 60 0 C µ 1.51 E 0.m D Q Using Snell s law µ 1 sin 5 µ sin θ θ 0. i.e. ray moves parallel to axis µ µ ( µ µ ) E E 6.056 m 6.06 m P B µ 1 1 µ 5 0 θ 0 0 60 0 C µ 1.51 E 0.m D Q 9. screw gauge of pitch 1mm has a circular scale divided into 100 divisions. he diameter of a wire is to be measured by above said screw gauge. he main scale reading is 1mm and 7 th circular division coincides with main scale. Find the curved surface area of wire in true significant figures. (Given the length of wire is equal to 5.6 cm and there is no zero-error in the screw gauge.) east count 1mm 0.01mm. 100 Diameter M. S. + No. of division coinciding with main scale east count. 1mm + 7 0.01 mm 1.7 mm 0.17 cm. Curved surface area πd 0.17 5.6.6 cm 7 10. he age of a rock containing lead and uranium is equal to 1.5 10 9 yrs. he uranium is decaying into lead with half life equal to.5 10 9 yrs. Find the ratio of lead to uranium present in the rock, assuming initially no lead was present in the rock. (Given 1/ 1.59) t/1/ 1/ NU 1 1 1 N 1.59 NU 1 N + N 1.59 Pb U U NPb 0.59 N. FIIJEE td. ICES House, Sarvapriya Vihar (Near Hauz Khas Bus erm.), New Delhi - 16, Ph : 686 518, 696566, 685 10, 651599 Fax : 6519
II-JEE 00-M- 11. n inductor of inductance () equal to 5 mh and resistance () equal to 11 Ω are connected in series to an C source. he rms voltage of a.c. source is 0 volts and frequency is 50 Hz. V ωt (a) Find the peak value of current in the circuit. (b) Plot the current (I) vs (ωt) curve on the given voltage vs (ωt) curve. (Given π 7 ) Z ( ω ) + V0 0 V I 0 0mp Z (100π 5 10 ) + (11) φ ω 100π 5 10 tan φ 11 φ 5 0 π I I 0 sin (ωt - ) π 0 sin (100 πt - ) 1 V π/ I V + V V I ωt 1. wo identical blocks and B are placed on a rough inclined plane of inclination 5 0. he coefficient of friction between block and incline is 0. and that of between B and incline is 0.. he initial separation between B the two blocks is m. he two blocks are released from rest, then find (a) the time after which front faces of both blocks come in same line and (b) the distance moved by each block for attaining above position. 5 0 µb 0. µ 0. m a g sin 5 0.g cos 5 m/s 7 a B g sin 5 0. g cos 5 m/s a B 0.5 m/s 1 s B a B t t 0.5 t sec. s B 1 a t 7 m B 1 s a t 8 m 1. In a photoelectric setup, the radiations from the Balmer series of hydrogen atom are incident on a metal surface of work function ev. he wavelength of incident radiations lies between 50 nm to 700 nm. Find the maximum kinetic energy of photoelectron emitted. (Given hc/e 1 ev-nm). FIIJEE td. ICES House, Sarvapriya Vihar (Near Hauz Khas Bus erm.), New Delhi - 16, Ph : 686 518, 696566, 685 10, 651599 Fax : 6519
II-JEE 00-M-5 1 1 hc 1 E 1.6 n eλ λ 1 n λ 1.6(n ) λ min which lies between 50 nm and 700 nm is for transition from n to n and is equal to 87.05 nm For maximum K.E. of photoelectron hc φ K.E. max λmin K.E max 1.6 1 0.55eV. 16 1. spherical ball of radius, is floating in a liquid with half of its volume submerged in the liquid. Now the ball is displaced vertically by small distance inside the liquid. Find the frequency of oscillation of ball. estoring force π xρg (for small x) d x m π xρ g dt d x g π x, (as ρ g mg ) dt Motion is SHM ω g 1 g f. π x 15. he two batteries and B, connected in given circuit, have equal e.m.f. E and internal resistance r 1 and r respectively (r 1 > r ). he switch S is closed at t 0. fter long time it was found that terminal potential difference across the battery is zero. Find the value of. E, r1 E, r B C S Since average voltage across capacitor and inductor for D.C. sources will be zero at steady state. E E I... (i) (eq + r1 + r ) (r1 + r + ) P.D. across the battery E Ir 1 0 I E/r 1... (ii) From (i) and (ii), (r1 r ) 16. point object is moving with velocity 0.01 m/s on principal axis towards a convex lens of focal length 0. m. When object is at a distance of 0. m from the lens, find (a) rate of change of position of the image, and (b) rate of change of lateral magnification of image. FIIJEE td. ICES House, Sarvapriya Vihar (Near Hauz Khas Bus erm.), New Delhi - 16, Ph : 686 518, 696566, 685 10, 651599 Fax : 6519
II-JEE 00-M-6 1 1 1 f v u 1 dv 1 du + 0 v dt u dt dv v du dt u dt.... (i) 1 1 1 0 v 0 v 10 cm. dv v v m 1 du u f dm v dv 1 dt f f dt 10 1 0.09 1.8 s 0. 0 1 u 0 0.01 m/s 0. m f 0.m 17. n experiment is performed to verify hm s law using a resister of resistance 100Ω, a battery of 6 - variable potential difference, two galvanometers and two resistances of 10 Ω and 10 Ω are given. Draw the circuit diagram and indicate clearly position of ammeter and voltmeter. Voltmeter 10 6 Ω G 100 Ω G 10 - Ω mmeter 18. uniform rod of length, conductivity K is connected from one end to a furnace at temperature 1. he other end of rod is at temperature and is exposed to atmosphere. he temperature of atmosphere is s. he lateral part of rod is insulated. If s << s, s + & ( 1 s ), find proportionality constant of given equation. he heat loss to atmosphere is through radiation only and the emissivity of the rod is ε. Furnace Insulation 1, K, ε s ( ) ( s ) K 1 εσ ( ) s εσ + s εσs ( 1 S) K K S σε + K( 1 S) K σε S + K Proportionality constant. K σε S + FIIJEE td. ICES House, Sarvapriya Vihar (Near Hauz Khas Bus erm.), New Delhi - 16, Ph : 686 518, 696566, 685 10, 651599 Fax : 6519
II-JEE 00-M-7 19. cubical block is floating inside a bath. he temperature of system is increased by small temperature. It was found that the depth of submerged portion of cube does not change. Find the relation between coefficient of linear expansion (α) of the cube and volume expansion of liquid (γ). x Coeff. f linear expn. α Coeff. of volume expn. γ t initial temperature for the equilibrium of the block ρ b g xρ g ρ b xρ... (i) t final temperature (1 + α ) ρ ρ (1 γ ) For the equilibrium of the block (1 + α )(x) ρ (1 γ ) ρ b xρ 1 + α γ 1 γ α 0. In a Young s double slit experiment light consisting of two wavelengths λ 1 500 nm and λ 700 nm is incident normally on the slits. Find the distance from the central maxima where the maximas due to two wavelengths coincide for the first time after central maxima. (Given D 1000 d ) where D is the distance between the slits and the screen and d is the separation between the slits. y 1 y ndλ 1 d mdλ d y 1 y n 7 m 5 For the first location, m 5, n 7 y 7 1000 5 10-7 5 10 -.5 mm. Note: FIIJEE solutions to II JEE, 00 Main Papers created using memory retention of select FIIJEE students appeared in this test and hence may not exactly be the same as the original paper. However, every effort has been made to reproduce the original paper in the interest of the aspiring students. FIIJEE td. ICES House, Sarvapriya Vihar (Near Hauz Khas Bus erm.), New Delhi - 16, Ph : 686 518, 696566, 685 10, 651599 Fax : 6519