when the particle is moving from D to A.

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Wesley Small
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1 PRT PHYSICS THE GRPHS GIVEN RE SCHEMTIC ND NOT DRWN TO SCE. student measures the time period of oscillations of a simple pendulum four times. The data set is 9s, 9s, 95s and 9s. If the minimum diision in the measurin clock is s, then the reported mean time should be: () 9 s () 9 5. s () 9.8 s 9 s Sum of all obseration = = 68 aerae = 68 9 Sum of modulus errors = + + = = 6 aerae error = 6.5, rounded of. final ans. = 9 s. particle of mass m is moin alon the side of a square of side a, with a uniform speed in the x-y plane as shown in the fiure : m Rkˆ when the particle is moin from D to. Solution : ( or ) s per each choice m () Rkˆ () R m a kˆ () R m a kˆ m Rkˆ. point particle of mass m, moin alon the uniformly rouh track PQR as shown in the fiure. The coefficient of friction, between the particle and the rouh track equals. The particle is released, from rest, from the point P and it comes to rest at a point R. The eneries, lost by the ball, oer the parts, PQ and QR, of the track, are equal to each other, and no enery is lost when particle chanes direction from PQ to QR. The alues of the coefficient of friction and the distance x(=qr), are, respectiely close to: Which of the followin statements is false for the anular momentum about the oriin? m () Rkˆ when the particle is moin from to B () R m a kˆ when the particle is moin from C to D. () R m a kˆ when the particle is moin from B to C. (). and 6.5 m (). and.5 m ().9 and.5 m.9 and 6.5 m Solution : () s enery loss is same, thus m cos. (PQ) = m.(qr) QR =.5m Equation after enery consideration is reduction in PE = loss due to friction

2 m = m m person tryin to lose weiht by burnin fat lifts a mass of k upto a heiht of m times. ssume that the potential enery lost each time he lowers the mass is dissipated. How much fat will he use up considerin the work done only when the weiht is lifted up? Fat supplied.8 7 J of enery per k which is conerted to mechanical enery with a % efficiency rate. Take = 9.8 ms : ().5 k () 6.5 k () 9.89 k.89 k Work done in liftin mass = ( 9.8) If m is mass of fat burnt, then enery 7 = m.8 = m.89 k.8 5. roller is made by joinin toether two cones at their ertices O. It is kept on two rails B and CD which are placed asymmetrically (see fiure), with its axis perpendicular to CD and its centre O at the centre of line joinin B and CD (see fiure). It is ien a liht push so that is starts rollin with its centre O moin parallel to CD in the direction shown. s it moes, the roller will tend to : () turn left () turn riht () o straiht turn left and riht alternately The radius of the left side oes as reducin due to conical shape. Hence left side coers lesser and lesser distance ( r, s dt). Thus the structure turns left. 6. satellite is reolin in a circular orbit at a heiht h from the earth s surface (radius of earth R; h >> R). The minimum increase in its orbital elocity required, so that the satellite could escape from the earth s raitational field, is close to : (Nelect the effect of atmosphere). () R () R () R / R( ) orbital GM R escape R R extra elocity required = R 7. pendulum clock loses s a day if the temperature is ºC and ains s a day if the temperature is ºC. The temperature at which the clock will show correct time, and the coefficient of linear expansion () of the metal of the pendulum shaft are respectiely: () 5ºC; =.85 5 / ºC () 6ºC; =.85 / ºC () ºC; =.85 / º C 55ºC; =.85 / ºC T T ' T T T' = T T ( ) = ( ) = T T. T T T T pplyin data T T T T T ( T ) T

3 T = T = 5ºC 8. n ideal as underoes a quasi static, reersible process in which its molar heat capacity C remains constant. If durin this process the relation of pressure P and olume V is ien by PV n = constant, then n is ien (Here C p and C are molar specific heat at constant pressure and constant olume, respectiely) : Cp C Cp () n () n C C C Cp C C C () n n C C C C Solution : () Q U W. s the process is polytropic NR( T ) NCT NCT n R CC n Cp C n C C Cp C n C C = ( C C ) ( C C ) C C C C C C p p 9. n moles of an ideal as underoes a process B as shown in the fiure. the maximum temperature of the as durin the process will be : () 9PV nr () 9PV nr Usin similar V V V V V P P P P P P P V V V ( ) P () PV nr 9PV nr p V P PV P T P V.V nr V P P ( ) P P V V V V P = PV V dt for hihest temperature dv PV P V P V V & P P P P V 9PV T may nr nr. particle perform simple harmonic motion with amplitude. Its speed is trebled at the instant that it is at a distance from equilibrium position. The new amplitude of the motion is : () () () V x at x 7 5. as elocity is lebled, hence ' 5 This leads to new amplitude ' ' 5 [ ' ] ' ' = 7. uniform strin of lenth m is suspended from a riid support. short wae pulse is introduced at its lowest end. It starts moin up the strin. The time taken to reach the support is : (take = ms ) () s () s () s s

4 Solution : () mx T m dx x dt / t / l x dx dt x / x t. t t sec.. The reion between two concentric spheres of radii a and b, respectiely (see fiure), has olume chare density, where r is a constant and r is the distance from the centre. t the centre of the spheres is a point chare Q. The alue of such that the electric field in the reion between the spheres will be constant, is : b a = Q. b Q Q a( b a ) a b a Q a( b a ) a Q a. combination of capacitors is set up as shown in the fiure. The manitude of the electric field, due to a point chare Q (hain a chare equal to the sum of the chares on the F and 9 F capacitors), at a point distant m from it, would equal : () N/C () 6 N/C () N/C 8 N/C () () Q a Q ( a b ) () Q ( b a ) Q a s E is constant, hence E a = E b b K[ Q r dr. ] kq a r a b b b r Q Q a a Solution : () F and 9F = F F & F = F F & F = 5F Q = 8 5 = C Final chare as F and 9F = + 8 = C 9 6 kq 9 E N/C R. The temperature dependence of resistances of Cu and undoped Si in the temperature rane K, is best described by : () inear increase for Cu, linear increase for Si. () inear increase for Cu, exponential increase for Si. () inear increase for Cu, exponential decrease for Si. inear decrease for Cu, linear decrease for Si.

5 Solution : () Fractional Q. We know for Cu, resistance increases linearly, but for semiconductors resistance falls exponentially. Option () is correct. 5. Two identical wires and B, each of lenth l carry the same current I. Wire is bent into a circle of radius R and wire B is bent to form a square of side a. If B and B B are the alues of manetic field at the centres of the circle and square respectiely, then the B ratio B is : () () B 8 6 () 6 8 B due to circle = I R B due to square I = sin 5º sin 5º l. = I l Now R & l Where = lenth of wire. I I I B. I 8 I 8 I B ratio = :8 6. Hysteresis loops for two manetic materials and B are ien below : These materials are used to make manets for electric enerators, transformer core and electromanet core. Then it is proper to use : () for electric enerators and transformers. () for electromanets and B for electric enerators. () for transformers and B for electric enerators. B for electromanets and transformers. We need hih retentiity & hih coerciity for electromanets & small area of hysterisis loop for transformers. 7. n arc lamp requires a direct current of at 8 V to function. If it is connected to a V (rms), 5 Hz C supply, the series inductor needed for its to work close to : () 8 H ().8 H (). H.65 H R V V V 8 V V 8 V V V V X W =.65 H 5 8. rrane the followin electromanetic radiations per quantum in the order of increasin enery : : Blue liht B : Yellow liht C : X-ray D : Radiowae () D, B,, C (), B, D, C () C,, B, D B,, D, C Factual question. Radiowae has lare waelenth, low frequency & hence low enery X-ray has ery hih enery. Rest are in between.

6 9. n obserer looks at a distant tree of heiht m with a telescope of manifyin power of. To the obserer the tree appears : () times taller () times nearer () times taller times nearer Solution : () manification = h i h imae is times taller than object.. The box of a pin hole camera, of lenth, has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of liht of waelenth the spread of the spot (obtained on the opposite wall of the camera) is the sum of its eometrical spread and the spread due to diffraction. The spot would then hae its minimum size (say b min ) when : () a and bmin () a and b min () a and bmin Solution : () a and bmin Spot size (diameter) a ab... (i) For real roots b bmin by equation (i) a b a a c h h m... () when waelenth decrease, then c h h m'... () hc E, then () + () E h ' E h '. Half-lies of two radioactie elements and B are minutes and minutes, respectiely. Initially, the samples hae equal number of nuclei. fter 8 minutes, the ratio of decayed numbers of and B nuclei will be : () : 6 () : () : 5 : /N N/ N/ N/8 N/6 B/N N/ N/ 5 N 6 decay of B = N ratio = (5 /6) 5: ( / ). If a, b, c are inputs to a ate and x is its output, then as per the followin time raph, the ate is :. Radiation of waelenth, is incident on a photocell. The fastest emitted electron has speed. If the waelenth is chaned to, the speed of the fastest emitted electron will be : () () () Solution : () () NOT () ND () OR NND

7 O state is in all sinals in the st step. In all strep some sinal hae state. The output has O as first step & I in all other steps. Hence OR ate.. Choose the correct statement: () In amplitude modulation the amplitude of the hih frequency carrier wae is made to ary in proportion to the amplitude of the audio sinal. () In amplitude modulation the frequency of the hih frequency carrier wae is made to ary in proportion to the amplitude of the audio sinal. () In frequency modulation the amplitude of the hih frequency carrier wae is made to ary in proportion to the amplitude of the audio sinal. In frequency modulation the amplitude of the hih frequency carrier wae is made to ary in proportion to the frequency of the audio sinal. Factual question. In amplitude modulation m c 5. screw aue with a pitch of.5 mm and a circular scale with 5 diisi8ons is used to measure the thickness of a thin sheet of luminum. Before startin the measurement, it is found that when the two jaws of the screw aue are brouht in contact the 5 th diision coincides with the main scale line and that the zero of the main scale is barely isible. What is the thickness of the sheet if the main scale readin is.5 mm and the 5 th diision coincides with the main scale line? ().75 mm ().8 mm ().7 mm.5 mm Solution : () east cont pitch.5mm = no.of diisiononcircularscale 5 C =. e zero errow = 5 C =.5 mm Measured alue = main scale readin + screw uae readin zero error =.5 mm + {5. (.5)} mm =.8 mm 6. pipe open at both ends has a fundamental frequency f in air. The pipe is dipped ertically in water so that half of it is in water. The fundamental frequency of the air column is now. f f () () () f f l l l l Hence frequency remains same. 7. alanometer hain a coil resistance of ies a full scale deflection, when a current of m is passed throuh it. The alue of the resistance, which can conert this alanometer into ammeter iin a full scale deflection for a current of, is : (). () (). IR Rs I I s I is ery small, hence I R Rs. I 8. In an experiment for determination of refractie index of lass of a prism by i -, plot, it was found that a ray incident at anle 5º, suffers a deiation of º and that it emeres at anle 79º. In that case which of the followin is closest to the maximum possible alue of the refractie index? ().5 ().6 ().7.8 Solution : () i e º 5º 79º 7º any Sn S ( / ) n 9. Identify the semiconductor deices whose characteristics are ien below, in the order (a), (b), (c), (d) :

8 () Simple diode, Zener diode, Solar cell, iht dependent resistance () Zener diode, Simple diode, iht dependent resistance, Solar cell () Solar cell, iht dependent resistance, Zener diode, Simple diode Zener diode, Solar cell, Simple diode, iht dependent resistance Factual question: st raph is forward biased diode Second is of een diode includin reerse bias & breakdown. Third is of solar cell & lastly for liht dependent resistance.. For a common emitter confiuration, if and hae their usual meanins, the incorrect relationship between and is : () () () Solution : ( and ) I Ib Ic Ie b I c I I e c

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