( ) v v v / 2. vapparent GHz

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1 JEE MINS 7 SOLUTIONS PHYSICS. n obsee is moing with half the speed of light towads a stationay micowae souce emitting waes at fequency GHz. What isthe fequency of hte micowae measued by the obsee? (a). Ghz (b) 7. GHz (c) 5. GHz (d). GHz ns b ns. appaent appaent appaent appaent oiginal + obsee wae obsee wae 8 / / 8 + / GHz 4 7. GHz. The following obseations wee taken fo detemining suface tension T of wate by capillay method: diamete of capillay, D.5 x m ise of wate h.45 x m hg Using g 9. 8 m/s and the simplified elation T N / m, the possible eo in the suface tension is closest to (a).5 % (b).4 % (c) % (d).5 % ns b T hg N / m T h g + + T h g T %.58% T. Some enegy leels of a molecule ae shown in the figue. The atio of the waelength is gien by:

2 (a) (b) 4 (c) (d) 4 ns c 4 hc E + E hc E + E E / E 4. body of mass m kg is moing in a medium and expeiences a fictional foce F k. Its initial speed is m/s. If afte s its enegy is m, the alue of k will be 8 (a) kg s (b) 4 kg m (c) kg m s (d) kg m ns. b dv m kv dt Vi Vi V / dv m m kdt kt V i V k kgm 4 V 5. C p and C ae specific heats at constant pessue and constant olume espectiely. It is oseed that C p C a fo hydogen gas C p C b fo nitogen gas (a) a b (b) a 4b (c) a 8b (d) a b/4 ns b In the question specific heat capacity isgien (which is pe unit mass) and not mola heat capacity. By Maye's fomula. The mola mass fo H and N ae and 8 espectiely C p C R/ fo hydogen gas C p C R/8 fo nitogen gas 6. The moment of inetia of a unifom cylinde of length l and adius R about its pependicula bisecto is I. What is the atio of l/r such that the moment of inetia is minimum. (a) (b) (c) (d) Ml MR I + l u M ρ π R l Ml I + M l uρ π l fo I to be di Min dl e M ρ π ρ R l l e ρ π R /

3 7. adioactie nucleus with half life T, decays into a nucleus B. t t thee is no nucleus B. t sometime t, the atio of numbe of B to that of is.. Then, t is gien by log. (b) t T log. T T log (a) t T (c) t (d) t log log. log. ns a half life.69 / T at t n B ( T ) n ( B) n ( ) at time t. By using N Ne t decayed n ( B ) N N N ( e ) emaining n N e t t N log. t log(.) log(.) t. T/ T.69 log 8. Which of the following statements is false (a) In a balanced wheatstome bidge if the cell and the galanomete ae exchanged the null point is distubed (b) heostat can be used a potential diide (c) Kichhoff's second law epesents enegy conseation (d) Wheatstone bidge is the most sensitie when all the fou esistance ae of the same ode of magnitude ns a On exchange of cell and galanomete null point is not distubed 9. capacitance of μf is equied in an electical cicuit acoss a potential diffeence of. KV. lage numbe of μf capacitos ae aailable which can withstand a potential diffeence of not moe than. The minimum numbe of capacitos equied to achiee this is (a) 6 (b) 4 (c) (d) ns c fo C µ F V. olt eq fo Caailable µ F V olt By using µ F capacitance we make µ F equialent capacitance st nd So we use capacito of µ F to make µ F equialent capacitance. 8th. In the gien cicuit diagam when the cuent eaches steady state in the cicuit the chage on the capacito of capacitance C will be :

4 ns b (a) CE + (b) CE + (c) CE + (d) CE. In the aboe cicuit the cuent in each esistance is (a).5 (b).5 (c) (d) ns c Hee potential diffeence between point -', B-B' and C-C' (points nea two batteeis in each loop)is zeo, So cuent acoss esistance is also zeo.. In amplitude modulation, sinusoidal caie fequency used is denoted by ω c and and the signal fequency is denoted by ω m. The bandwidth (Δω m ) of the signal is such that Δω m <<Δω c. Which of the following fequencies is not contained in hte modulted wae? (a) ω c (b) ω c + ω m (c) ω c - ω m (d) ω m ns d Fequency of caie wae w c fequency of signal w m Spectum of modulated wae w m w c w m w c w c + w m w m. In a common emitte amplifie cicuit using an n-p-n tansisto, the phase diffeence between the input and the output oltages will be (a) 9 (b) 5 (c) 8 (d) 45 ns. c In common emitte amplifie cicuit Vout RL Voltage gain β. Vin So phase diffeence between input and output is coppe ball of mass gm is at a tempeatue T. It is dopped in a coppe caloimete of mass gm, filled with 7 gm of wate at oom tempeatue. Subsequently the tempeatue of the system is found to be 75 C. T is gien by: Gien oom tempeatue C. Specific heat of coppe. cal/gm C (a) 885 C (b) 5 C (c) 85 C (d) 8 C ns. m coppe ball gm T coppe ball T

5 m coppe coloimete gm {T C} m wate 7 gm Final tempeatue T f 75 C S wate cal/gm - C Heat lost Heat gain m coppe ball. S c.b.(t T f ) m c.c.s cc (T f ) + m w.s w (T f ). (T-75). (75-)+7 (75-) (T-75) T T 885 C 5. In a Youngs double slit expeiment slits ae sepaated bu.5 mm, and the sceen is placed 5 cm away. beam of light consisting of two waelengths 65 nm and 5 nm, is used to obtain intefeence finges on the sceen. The least distance fom the common cental maximum to the point whee the bight finges due to both the waelength coincide is. (a) 7.8 mm (b) 9.75 mm (c) 5.6 mm (d).56 mm ns. a d.5 mm, D 5 cm 65 nm and 5 nm fo maxima x D xn d fi x fo x.5.5 we take p th maxima fo and q th maxima fo x p x x q x p q p 5 4 q 65 5 So, distance fom cental maxima x 4 7.8mm.5 6. n electic dipole has a fixed dipole moment P, which makes angle θ wiht espect to x axis. When subjected to an electic field E Ei, it expeiences a toque T τk. When subjected to anothe electic field E Ej it expeiences a toque T -- T The angle θ is (a) 45 (b) 6 (c) 9 (d) ns. b y +q 9-θ θ x -q Z P E whee P is dipole moment and E is electic field fo E Eiˆ P( E)sin θ τ ( i) fo E Ej ˆ P E cos θ τ ( ii) By eq (i) & (ii)

6 tanθ θ 6 7. slende unifom od of mass M and length l is pioted at one end so that it can otate in a etical plane., Thee is negligible fiction at the piot. The tee end is held etically aboe the piot and then eleased. The angula acceleation of the od when it makes an angle θ with the etical is (a) g sin θ l (b) g cos θ l (c) g cos θ l (d) g sin θ l θ mg sin θ mg l ml t mg sin θ Iα whee I α 9 sin θ l 8. n extenal pessue P is applied on a cube at C so that it is equally compessed fom all sided. K is the bulk modulus of the mateial of the cube and α is its coefficient of linea expansion. Suppose we want to bing the cube to its oiginal size by heating. The tempeatue should be aised by (a) P (b) α (c) PK α (d) P α K PK α K Hee stess deeloped by extenal pessue is equal but opposite to stess deeloped due to aise in tempeatue. By pessue By tempeatue K P V / V F / K. T we know α P K. ( α ).( Tf ) T f P α K 9. dieging lens with magnitude of focal length 5 cm is placed at a distance of 5 cm fom a coneging lens of magnitude of focal length cm. beam of paallel light falls on the dieging lens. The final image fomed is (a) itual and at a distance of 4 cm fom conegent lens (b) eal and at a distance of 4 cm fom the diegent lens (c) eal and at a distance of 6 cm fom the conegent lens (d) eal and at a distance of 4 cm fom conegent lens ns. 4 Image (I ) fomed by dieging lens act as a object fo coneging lens and final image is fomed by coneging lens. i. Vitual Image (I ) is fomed at focus of dieging lens

7 ii. Object distance fo coneging lens is F. iii. So finally eal image at F is fomed by coneging lens.. n electon beam is acceleated by a potential diffeence V to hit a metallic taget to poduce X ays. It poduces continuous as well as chaacteistics X-ays. If min is the smallest possible waelength of X-ay in the spectum the aiation of log min with logv is coectly epesentsed in (a) (b) (c) (d) log min hc min e max log V.75 o in olt on taking logithmic log min log75 log im. The tempeatue of a an open oom of olume m inceases fom 7 C to 7 C due to the sunshine, The atmospheic pessue in the oom emains x 5 Pa. If n i and n f ae the nunbe of molecules in the oom befoe and afte heating, then n f n i will be (a).8 x (b).5 x 5 (c) -.5 x 5 (d) -.6 x ns. c Initially 5 Ti 7 C, Vi m, pi Pa, ni atm Finally T 7 C, V m, P 5 Pa, n f f f e we know that

8 PV PV nrt n RT Pf V f PV i i n f ni RT RT n f f 5 ni 8. 9 no. of molecules whee N molecules i n n N f i. In a coil of esistance ohm, a cuent is induced by changing the magnetic flux though it as shown in the figue. The magnitude of change in flux though the coil is (a) 5 Wb (b) 5 Wb (c) 75 Wb (d) Wb ns. b R Ω dφ emf ( e) dt φ edt we know e i.r. φ R idt φ.5 φ 5Wb. When a cuent of 5m is passed though a galanomete haing a coil of esistance 5 ohm its shows a full scale deflection. The alue of the esistance to be put in seies with the galanomete to conet it into oltmete of ange V is (a).45 x (b).55 x (c) 4.5 x (d).985 x G 5Ω Full deflection at 5m oltmete of ange olt I g.(g + R) V R R 5 R.985 Ω 4. time dependent foce F 6t acts on a paticle of mass kg. If the paticle stats fom est the wok done by the foce duing the fist sec will be (a) J (b) 9 J (c) 8 J (d) 4.5 J

9 F 6t a F m 6t adt 6tdt W W KE 4.5 Joule 5. magnetic needle of magnetic moment 6.7 X m and moment of inetia 7.5x-6 kgm is pefoming SHM in a magnetic field of.t. Time taken fo complete oscillations is (a) 8.89 s (b) 6.98 s (c) 8.76 s (d) 6.65 s magnetic moment (m) 6.7 m 6 moment of inetia (I) 7.5 kgm magnetic field (B). T T π J mb T π time taken to complete to oscillation t T t 6.65sec 6. The aiaion of acceleation due to gaity g with distance d fom cente of the eath is best epesnted by (a) (b) (c) (d) ns. c g O R d we know that at outside on suface at inside GM e GM e G. M. g g suface g in R R e e 7. body is thown etically upwads. Which one of the following gaphs coectly s time? (a) (b) (c) (d)

10 ns b In upwad diection elocity is positie and continously deceasing till the paticle eaches maximum height whee it becomes zeo. In its downwad jounedy elocity is in negatie diection and continuously inceasing. 8. paticle of mass m and initial elocity collides with a paticle B of mass m/ which is at est. The collision is head on and elastic. The atio of de-boglies walegths and B afte the collision is (a) (b) B ns a By momentum conseation m m m h h. m m B (c) B (d) 9. paticle is executing simple hamonic motion with a time peiod T. t time t, it is at tis position of equilibium. The kinetic enegy- time gaph of the paticle will look like B (a) (b) (c) (d) ns c at t, T/ paticle at mean position and kinetic enegy should be maximum at t T/4, T/4 Paticle at ex steam position and kinetic enegy should be minimum. man gows into a giant such that his linea dimensions incease by a facto of 9. ssuming that his density emains same, the stess in the leg will change by a facto of (b) 8 (d) 9 (a) (c) 9 8 ns d

11 STY WITH US WE RE CONTIOUSLY UPLODING THE SOLUTIONS

15 B1 1. Figure 1. At what speed would the car have to travel for resonant oscillations to occur? Comment on your answer.

15 B1 1. Figure 1. At what speed would the car have to travel for resonant oscillations to occur? Comment on your answer. Kiangsu-Chekiang College (Shatin) F:EasteHolidaysAssignmentAns.doc Easte Holidays Assignment Answe Fom 6B Subject: Physics. (a) State the conditions fo a body to undego simple hamonic motion. ( mak) (a)