PHYSCS PCTCE POLEMS Exam fom 6 th to 6 th May 9. n a ace fo m dash, the fist and the second unnes have a gap of one mete at the mid way stage. ssuming the fist unne goes steady, by what pecentage should the second unne incease his speed just to win the ace? (a) % (b) % moe than % less than %. sand bag of mass m is suspended fom a long sting. bullet of mass m moving with a hoizontal velocity v stikes it and gets embedded into it. Calculate the velocity gained by the bag in this pocess and faction of enegy lost in the pocess. v v 8 (a) ; (b) ; v v ; ; 9. The bodies situated on the suface of eath at its equato, become weightless, when the kinetic enegy of otation of eath about its axis is (a) Mg (b) Mg/ Mg/ Mg/. Two linea SHMs of equal amplitude and angula fequencies w and w ae impessed on a paticle along the axes x and y espectively. f the initial phase diffeence between them is p/, the esultant path followed by the paticle is (a) y x ( x / ) (b) y x ( x / ) y x ( x / ) y 8x ( x / ). caloie is a unit of heat and equals. J. Suppose we employ a system of units in which the unit of mass is a kg, the unit of length is b m and the unit of time is g s. n this new system, caloie will be (a) a b g (b).ab g ab g.a b g 6. Which of the following gaph epesents the vaiation of magnetic flux density with distance fo a staight long wie caying an electic cuent? (a) (b) 7. n an L cicuit, the value of L is (./p) H and the value of is W. f in the cicuit, an altenating emf of V at cycle pe second is connected, the impedance of the cicuit and cuent will be (a). W, 7. (b).7 W, 6.. W, W, 8. micoscope has an objective of focal length. cm and eyepiece of focal length. cm. f the distance between objective and eyepiece is cm, what is the appoximate value of magnification poduced fo elaxed eye? (a) 7 (b) 9. Two small conducting sphees of equal adius have chages + mc and mc and placed at a distance fom each othe expeience foce F. f they ae bought in contact and sepaated to the same distance, they expeience foce F. The atio of F to F is (a) : (b) 8 : : 8 :. Two masses kg and kg ae connected by a weightless sting passing ove a fictionless pulley as shown in the figue. The tension in the sting will be (a) 88 N (b) 68 N 88 N 68 N. t constant tempeatue, the volume of a gas is to be deceased by %. The pessue must be inceased by (a).% (b).6%.96%.86%
. n a Young's double slit expeiment, one of the slits is coveed with a tanspaent sheet of thickness.6 m due to which position of cental bight finge shifts to a position oiginally occupied by th finge. The efactive index of the sheet, if l 6 Å, is (a). (b).9..7. t time t, activity of a adioactive substance is 6 q, at t 8 s activity becomes q. Find the activity at t s. (a) q (b) q 6 q 8 q. Find the atio of minimum to maximum enegy of adiation emitted by electon in gound state of oh's hydogen atom. (a) (b). n an expeiment with sonomete, a tuning fok of fequency 6 Hz esonates with a length of cm and anothe tuning fok esonates with a length of 6 cm. Tension in the sting emains constant, the fequency of the second tuning fok is (a) Hz (b) 6 Hz Hz Hz 6. efe to the aangement of logic gates. Fo, and,, the values of output Y ae, espectively Y (a) and (b) and and and 7. f the length of stetched sting is shotened by % and the tension is inceased by %, then the atio of the final and initial fundamental fequencies is (a) : (b) : : : 8. V input is supplied to a tansfome. The output cicuit daws a cuent of. at V. f the efficiency of the tansfome is 8%, the cuent dawn by the pimay windings of the tansfome is (a).6 (b).8.. 9. When a metal suface is illuminated with light of wavelength l, the stopping potential is V. When the same suface is illuminated with light of wavelength l, the stopping potential is V. f the velocity of light in ai is c, the theshold fequency of photoelectic emission is c c c c (a) (b) 6λ λ λ λ. launching vehicle caying an atificial satellite of mass m is set fo launch on the suface of the eath of mass M and adius. f the satellite is intended to move in a cicula obit of adius 7, the minimum enegy equied to be spent by the launching vehicle on the satellite is (Gavitational constant G) (a) (b) 7. n inductance coil is connected to an ac souce though a 6 W esistance in seies. The souce voltage, voltage acoss the coil and voltage acoss the esistance ae found to be V, 7 V and V espectively. Theefoe, the esistance of the coil is (a) W (b) W W 7 W. The cylindical tube of spay pump has a cosssection of 8 cm, one end of which has fine holes each of aea 8 m. f the liquid flows inside the tube with a speed of. m min, the speed with which the liquid is ejected though the holes is (a) m s (b) m s. m s. m s. body is fied vetically upwads. t half the maximum height, the velocity of the body is m s. The maximum height aised by the body is (Take g m s ) (a) m (b) m m m. f the masses of deuteium and helium ae. amu and.6 amu, espectively and. MeV enegy is libeated in the eaction 6 6 Li + H He + He, the mass of Li is (a) 6. amu (b) 6.68 amu.98 amu 6. amu. The maximum ange of pojectile fied with some initial velocity is found to be m, in the absence of wind and ai esistance. The maximum height eached by the pojectile is (a) m (b) m m m 6. n the adjoining figue, the equivalent esistance between and is (a) 7 Ω 7 Ω (b) 8 6 6 Ω Ω
7. satellite in a cicula obit of adius has a peiod of hous. nothe satellite with obital adius aound the same planet will have a peiod (in hous) (a) 6 (b) 7 8 8. body of mass M suspended fom two spings sepaately executes simple hamonic motion. Duing oscillation the maximum velocity is equal in both cases. The atio of amplitude is (a) (b) 9. unifom thin ba of mass 6m and length L is bent to make a egula hexagon. ts moment of inetia about an axis passing though the cente of mass and pependicula to the plane of hexagon is (a) ml (b) 6mL ml ml. n object is displaced fom position vecto ( ^ i + ^ j) m to ^ i ^ ( + 6 j ) m unde a foce F ( x ^ ^ i + y j) N. The wok done by this foce is (a) 6 J (b) 7 J 8 J 9 J. chage Q is enclosed by a gaussian spheical suface of adius. f the adius is doubled, then the outwad electic flux will (a) incease fou times (b) be educed to half emain the same be doubled. small bulb emits W of electomagnetic adiation unifomly in all diections. What is the maximum enegy density in the electic field at a point. m fom the souce? (a). 8 J m (b). 8 J m.6 8 J m. 8 J m. n an intefeence patten poduced by two identical slits, the intensity at the site of the cental maximum is. The intensity at the same spot when eithe of the two slits is closed is. Theefoe, (a) (b) and ae not elated to each othe.. n an L- ciuit shown in figue, L switch S is closed at time t. f e denotes the induced emf acoss V S inducto and, the cuent in the cicuit at any time t, then which of the following gaphs, shows the vaiation of e with? (a) (b). The time of vibation of a dip needle vibating in the vetical plane in the magnetic meidian is s. When the same magnetic needle is made to vibate in the hoizontal plane, the time of vibation is s. Then the angle of dip is (a) (b) 6 9 6. cuent of flows in the system of conductos as shown in the figue. The potential diffeence V P V will be nealy P (a) V (b) V S + V Q + V 7 7. When the evese potential in the semiconducto diode ae V and V, the coesponding evese cuents ae m and m espectively. The evese esistance of junction diode will be (a) kw (b) kw kw none of these 8. metal od of Young s modulus Y and coefficient of themal expansion a is held at its two ends such that its length emains invaiant. f its tempeatue is aised by t C, the linea stess developed in it is αt Y (a) (b) Yat Y αt ( Yαt) 9. The deflection in a moving coil galvanomete falls fom divisions to divisions when a shunt of ohm is applied. What is the esistance of the galvanomete? (a) W (b) W 6 W 8 W. The angula momentum of an electon in the hydogen atom is h. Hee, h is Planck s constant. π The kinetic enegy of this electon is (a). ev (b). ev. ev 6.8 ev
SOLUTONS. : Let v, v be the initial speeds of fist and second unnes. Let t be the time taken by them when the fist unne has completed m. Duing this time, the second unne has coveed a distance 9 m. 9 So, t...(i) v v Suppose the second unne inceases his speed to v so that he coves the emaining distance ( m) in time t. So 9 t o v v + v v v 9 9 v o o v v v 9 v 9 o % incease %.% 9 i.e. moe than %. (a) : pplying pinciple of consevation of linea momentum, m m m v m + v v v v v This is the velocity gained by the bag. m nitial kinetic enegy of bullet, E v Final kinetic enegy of bag and bullet, E m m m v + v Loss of enegy m E E v m v E E Faction of enegy lost E. : When thee is a weightlessness in the body at the equato, then g g w o ω g / and linea velocity ω ( g/ ) g \ Kinetic enegy of otation of eath ω M ω M( ω) Mg. : x sin(wt + p/) cos wt \ cos wt x/ and sin ωt ( x / ) y sin wt sin wt cos wt o y sin wt cos wt x x x x. : caloie. J \ [caloie] [ML T ]. Compaing with geneal dimensional fomula [M a L b T c ], we get a, b, c a b c M n n L T M L T n. kg m s αkg βm γ s. a b g 6. : Magnetic field induction at a point due to a long cuent caying wie is elated with distance by elation /. Theefoe gaph is coect. 7. : Hee, X L wl pul. π Ω π W \ Z + X L + Ω Vms ims Z 8. : Length of the tube is L v + f e v L f e.. cm Now applying, we have v u f. u. \ u.6 cm \ M v D u f e. 6.. k k 9. (b): Hee, F ( + )( ) s sphees ae of equal adius, thei capacities ae same. On touching, the net chage + mc is shaed equally between them i.e, each sphee caies mc chage. k( )( ) k F F \ 8 F. : a a
m gsin T m a... (i) T m gsin m a... (ii) dding (i) and (ii), mg mg a sin sin m+ m Fom eqn. (ii), we get T m g sin + m a m mg sin + ( mg sin mg sin ) m + m mm g sin 98. ( / ) m+ m + 98. 68 N 7. (b): t constant tempeatue, pv constant p V p V p V o p V Factional change in volume V V V V V o, V V p V p \ o p V p p p p % incease in pessue.6 %. (a) : The position of th λd bight finge y d λd New position of cental finge is y d ut we know, y shift due to tanspaent sheet D (µ )t d λd D So, ( µ ) t d d λ ( 6 ) ( µ ). t (. 6 ) \ m. n. : ctivity, whee n is the numbe of half-lives. t t 8 s, 6 n 6 n o n fou half-lives ae equivalent to 8 s. Hence, s is equal to one half-life. So, in one half-life activity will fall half of 6 q i.e., 8 q.. : Enegy of adiation coesponding to tansition between two enegy levels n and n is given by E. 6 n n ev. E is minimum when n and n. Hence, E min. 6 ev.6 ev E is maximum when n and n (when the atom is ionised). Hence E max. 6. 6 ev \ E min Emax. : Fo sonomete, fequency of vibation of sting, povided its tension and mass pe unit length emain same, is given by υ l υ \ l υ o υ l 6 6 6 υ Hz 6 6. (b): 7. (a) : nitial fundamental fequency of a stetched sting is υ T (i) L µ whee the symbols have thei usual meanings. When the length of a stetched sting is shotened by % and the tension is inceased by %, then its length and tension become L L L L, 6 T T + T T Then, final fundamental fequency is T 6 T T υ L µ (ii) µ L µ L Dividing (ii) by (i), we get υ υ Y Y
8. : Hee, V p V, s, V s V h 8%, p? η V s s V s s o p Vpp η Vp Substituting the given values, we get 9. (b) p 8. (b): The enegy of the satellite on the suface of the eath is Es + + KE PE The enegy of the satellite in an obit of adius is Eo mvo + m GM s vo GM The minimum enegy equied to be spent by the vehicle is E Eo Es 7 ( ) ( 7) +. (b). (b): ccoding to equation of continuity, a v a v 8. ( ) v 8 6 8 o v. ms 8 6. (b): Let h be maximum height eached by the body. Taking motion of the body fom half the maximum height upto the highest point, we have u m s, a g m s, v, S h s v u + as \ + ( ) h o h m. (a) : n the given eaction,.e. [(m( 6 Li) + m( H) m( He)] 9. \ m( 6 Li).. +.6 9 6. amu. (a) : ange, u sinθ g Fo maximum ange, angle of pojection q is. u sin( ) \ max u m (i) g g \ Maximum height, H u sin g H m (Using (i)) 6. (b) : The equivalent cicuit is as shown in figue. C G F 8 6 6 esistance of am G 8 + + 6.6 +. W 8 + 6 Fo equivalent esistance between and, the esistance of ams CD, G and FE ae in paallel. Thus 9 + + + + 6 o 9 Ω 7. : ccoding to Keple s thid law T T T / 7 / hous 8. : Fo SHM, Maximum velocity, v max w Fo st case, v k max ω...(i) M Fo nd case, v k max ω...(ii) M ccoding to question, v v max max D E
k M k o M k k 9. (a) : Length of each side of hexagon L Mass of each side m Let O be cente of mass of hexagon. Theefoe, pependicula distance of O fom each side O Ltan6 L The desied moment of inetia of hexagon about O is 6 6 [ one side ] L m( L) L 6 + m 6 ml ml + ml ( ) 6 + ml ml.. : ccoding to Gauss s law, the total outwad electic flux linked with gaussian suface φe ε chage enclosed by suface. f the adius of the gaussian suface is doubled the total outwad electic flux will emain the same as chage enclosed by the guassian suface is unchanged.. : Hee, P W,. m P ntensity of adiation at distance, π Let maximum enegy density in the electic field u Emax P Then ue c max π P o ue max π c 8. ( ) ( ).6 8 J m. : When one slit is closed, amplitude becomes half and intensity becomes / th i.e., o. : n L cicuit, cuent at any time t is given by V V V e L t e L t...(i) d V dt e L t V L L e L t nduced emf ε L d Ve L t...(ii) dt Fom (i), V Ve L t Using (ii), V e o e V Theefoe, gaph between e and is a staight line with negative slope and positive intecept.. : t π. (i) M whee is esultant intensity of eath s field t π (ii) MH Dividing eqn.(i) by eqn.(ii) H cos δ cos δ cos δ, δ 6 6. (b): esistance between Q and S, + Ω Potential diffeence acoss Q and S, VQ VS V Cuent though am QPS, VQ VP 8 V Cuent though am QS, / VQ V V V P V (V Q V ) (V Q V P ) 8 V. V 7. (b): evese esistance ( ) 6 W kw 8. : Due to change in tempeatue t C, incease in length, l l lαt o αt l
l stess stess Stess Y Yαt l stain l / l 9. : n case of a galvanomete, q So, G i.e., G Y Fom figue, ( G)S GG i.e., ( ) G o, G 8 W h h n \ n π π The kinetic enegy of the electon in nth obit is.6 K n ev n.6.6 ev. ev \ K ev 9 nn. (b) :