PHYSICS ÊÒÁà ÁflôÊÊŸ 1. A physical quantity P is described by the relation 1 3 4 P = a b c d If the relative errors in the measurement of a, b, c and d respectively, are %, 1%, 3% and 5%, then the relative error in P will be : 8% 1% 3% 5%. A car is standing 00 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration m/s and the car has acceleration 4 m/s. The car will catch up with the bus after a time of : 110 s 10 s 10 s 15 s 1. ÊÒÁà UÊÁ Ê P ÁŸêŸ œ mê UÊ Á U ÊÁ Ã Ë ÊÃË Ò 1 3 4 P = a b c d ÿᜠa, b, c ÊÒ U d apple Ê Ÿ apple Ê appleˇê òêèá U Ê %, 1%, 3% fl 5% Êapple ÃÊapple P apple Ê appleˇê òêèá U ÊappleªË 8% 1% 3% 5%. Ê U U UË ÈÿË apple 00 m Ë appleu π«ë Ò ŒÊappleŸÊapple Ë ˇÊáÊ ª- ª ª ÁŒÁ Ê àfl UáÊ apple ø ŸÊ ÊÈM UÃapple Ò Ê àfl UáÊ m/s ÃÕÊ Ê U Ê àfl UáÊ 4 m/s Ò Á ßapple ÿ ÊŒ ÿ Ê U Ã È ø ÊÿappleªË? 110 s 10 s 10 s 15 s 1 IX - PHYSICS
3. Two particles A and B of equal mass M are moving with the same speed v as shown in the figure. They collide completely inelastically and move as a single particle C. The angle θ that the path of C makes with the X-axis is given by : 3. ÊŸ Œ ÿ ÊŸ M apple ŒÊapple áê A ÃÕÊ B ÊŸ øê v apple ÁøòÊÊŸÈ Ê U ø U apple Ò fl ÍáÊ ÃÿÊ àÿêsõ ÉÊ^ UÃapple Ò ÃÕÊ ÉÊ^ apple ÊŒ áê C Ë Ã U ø Ãapple Ò ÊappleáÊ θ, Êapple áê C Ê Õ X- ˇÊ apple ŸÊÃÊ Ò, Êapple ÁŸêŸ ê 㜠apple ÁŒÿÊ ÊÿappleªÊ 3 + tanθ= 1 3 tanθ= 1 tanθ= 1 ( 1+ 3 ) 1 3 tanθ= 1 + 3 + tanθ= 1 3 tanθ= 1 tanθ= 1 ( 1+ 3 ) 1 3 tanθ= 1 + IX - PHYSICS
4. The machine as shown has rods of length 1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has a roller that rolls along the floor in a slot. As the roller goes back and forth, a kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a : 4. ÁøòÊ apple ÁŒπÊÿË ªÿË ÊËŸ Ë ŒÊapple U«Êapple, Á Ÿ Ë ê Êß 1 m Ò, apple UË Á UÊapple Êapple ÊÕ œè Uʪ Sà Á ÿê ªÿÊ Ò U«Ê ÊÁπ UË Á UÊ ÁSÕ U œè UË mê UÊ» Ê apple Êapple«Ê ªÿÊ Ò ÃÕÊ ŒÍ UË U«apple ÊÁπ UË Á appleu U UÊapple U ªÊ Ò Êapple Á» Ê U Ÿapple πê øapple apple ø ÃÊ Ò fl UÊapple U ʪapple Ë appleu ø ÃÊ Ò ÃÊapple kg Ê Ê U U ŸËøapple ø ÃÊ Ò ÿᜠUÊapple U ŒÊÁ ŸË ÁŒ ÊÊ apple ÊŸ øê apple ø ÃÊ Ò ÃÊapple fl Ê U ø appleªê, constant speed decreasing speed increasing speed speed which is 3 th of that of the 4 roller when the weight is 0.4 m above the ground ÊŸ øê apple ÉÊ UÃË Èß øê apple ÃË Èß øê apple øê Êapple Á UÊapple U Ë øê Ê 3 Ò fl 4 Ê U» Ê apple 0.4 m Ë øêß U Ò 3 IX - PHYSICS
5. A conical pendulum of length 1 m makes an angle θ=45 w.r.t. Z-axis and moves in a circle in the XY plane. The radius of the circle is 0.4 m and its center is vertically below O. The speed of the pendulum, in its circular path, will be : (Take g=10 ms ) 5. ÊÊ fl (conical) ŒÊapple, Á Ë ê Êß 1 m Ò ÊÒ U Êapple Z- ˇÊ apple θ=45 apple ÊappleáÊ U Ò, XY à apple ªÊapple Ê Ê U Õ apple ø ÃÊ Ò ªÊapple Ê Ê U Õ Ë ÁòÊíÿÊ 0.4 m Ò ÊÒ U Ê apple 㜠Á ãœè O apple UË ŸËøapple Ò ŒÊapple Ë ªÁà ªÊapple Ê Ê U Õ apple ÊappleªË (g=10 ms ) 0.4 m/s 4 m/s 0. m/s m/s 0.4 m/s 4 m/s 0. m/s m/s 4 IX - PHYSICS
6. A circular hole of radius R is made in a 4 thin uniform disc having mass M and radius R, as shown in figure. The moment of inertia of the remaining portion of the disc about an axis passing through the point O and perpendicular to the plane of the disc is : 6. Œ ÿ ÊŸ M ÃÕÊ ÁòÊíÿÊ R flê apple ÊŸ Á«US apple R ÁòÊíÿÊ Ê ªÊapple Ê Ê U appleuœ, ÁøòÊÊŸÈ Ê U, Á ÿê 4 ªÿÊ Ò Á ŒÈ O apple ÊŸapple flê apple ÃÕÊ Á«US apple à apple ê flã ˇÊ apple Ê appleˇê, Á«US apple øapple È Êª Ê, «àfl ÊÉÊÍáÊ ÊappleªÊ 19 MR 56 37 MR 51 19 MR 51 197 MR 56 19 MR 56 37 MR 51 19 MR 51 197 MR 56 5 IX - PHYSICS
7. The mass density of a spherical body is given by ρ (r)= k for r R and r ρ (r)=0 for r > R, where r is the distance from the centre. The correct graph that describes qualitatively the acceleration, a, of a test particle as a function of r is : 7. ªÊapple Ê Ê U Á á«u Ê Œ ÿ ÊŸ ÉÊŸàfl Ò ρ (r)= k r r R ÃÕÊ ρ (r)=0 r > R, Ê r apple 㜠apple ŒÍ UË Ò ÁŸêŸ apple apple ÊÒŸ Ê ª Ê$» UˡÊáÊ áê apple àfl UáÊ a Êapple r apple» Ÿ apple ªÈáÊÊà M apple Œ ÊÊ ÃÊ Ò? 6 IX - PHYSICS
8. A steel rail of length 5 m and area of cross section 40 cm is prevented from expanding along its length while the temperature rises by 10 C. If coefficient of linear expansion and Young s modulus of steel are 1. 10 5 K 1 and 10 11 Nm respectively, the force developed in the rail is approximately : 10 7 N 1 10 5 N 10 9 N 3 10 5 N 9. Two tubes of radii r 1 and r, and lengths l 1 and l, respectively, are connected in series and a liquid flows through each of them in stream line conditions. P 1 and P are pressure differences across the two tubes. If P is 4P 1 and l is l 1 4, then the radius r will be equal to : r 1 r 1 4r 1 r 1 8. 5 m ê Êß ÃÕÊ 40 cm ŸÈ SÕ Ê U apple ˇÊappleòÊ» Ë S UË Ë U UË Ê ê Êß apple ŸÈÁŒ Ê ÁflSÃÊ UáÊ UÊapple Ê ÊÃÊ Ò Á Ê ÃÊ ÊŸ 10 C ÊÿÊ ÊÃÊ Ò ÿᜠS UË Ê appleuπëÿ Ê U ªÈáÊÊ ÃÕÊ ÿ ª àÿêsõãê ªÈáÊÊ Ê 1. 10 5 K 1 ÃÕÊ 10 11 Nm Ò ÃÊapple U UË apple à ÛÊ Ê ÁŸ Uà ʟ ÊappleªÊ 10 7 N 1 10 5 N 10 9 N 3 10 5 N 9. ŒÊapple ŸÁ ÿê Á Ÿ Ë ÁòÊíÿÊÿapple Ê r 1 fl r ÃÕÊ ê Êß ÿê, l 1 fl l Ò, Êapple üêappleáêë apple Êapple«Ê ªÿÊ Ò ÊÒ U Ÿ apple Œ fl œê UÊ appleuπëÿ flê apple ÃÊ Ò Ë ÃÕÊ ŒÍ UË Ÿ Ë apple Á UÊapple apple Ëø apple ŒÊ Êãà U Ê P 1 ÃÕÊ P Ò ÿᜠP Ê ÊŸ 4P 1 ÃÕÊ l Ê ÊŸ 1 Êapple ÃÊapple ÁòÊíÿÊ 4 r Ê ÊŸ ÊappleªÊ r 1 l r 1 4r 1 r 1 7 IX - PHYSICS
10. For the P-V diagram given for an ideal gas, 10. ÊŒ Ê ªÒ Ê P-V Ê appleuπ ÁŒÿapple ªÿapple ÁøòÊ apple Œ ÊÊ ÿê ªÿÊ Ò out of the following which one correctly represents the T-P diagram? ÁŒÿapple ªÿapple Ê appleuπêapple apple apple ÊÒŸ- Ê Ë T-P Ê appleuπ Œ ÊÊ ÿappleªê? 8 IX - PHYSICS
11. N moles of a diatomic gas in a cylinder are at a temperature T. Heat is supplied to the cylinder such that the temperature remains constant but n moles of the diatomic gas get converted into monoatomic gas. What is the change in the total kinetic energy of the gas? 11. Ám U ÊáÊÈ ªÒ apple N Êapple T ÃÊ ÊŸ U Á appleá«u U apple Œ Ò Á appleá«u U apple c Ê ß Ê U flêá Ã Ë ÊÃË Ò Á apple Ám U ÊáÊÈ ªÒ apple n Êapple U ÊáÊÈ ªÒ apple Á ŸÊ ÃÊ ÊŸ Œ apple Á UflÁà à Êapple ÊÃapple Ò ªÒ Ë È ªÁÃ Ê apple Á ÃŸÊ Á Uflà Ÿ ÊappleªÊ? 0 1 nrt 3 nrt 5 nrt 1. A block of mass 0.1 kg is connected to an elastic spring of spring constant 640 Nm 1 and oscillates in a damping medium of damping constant 10 kg s 1. The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to : s 3.5 s 5 s 7 s 0 1 nrt 3 nrt 5 nrt 1. 0.1 kg Œ ÿ ÊŸ apple ªÈ U apple Êapple àÿêsõ ÁS ª, Á Ê ÁS ª ÁŸÿÃÊ 640 Nm 1 Ò, apple Êapple«Ê ªÿÊ Ò ÿ ªÈ U Ê fl ãœÿ Êäÿ, Á Ê fl ãœÿ ªÈáÊÊ 10 kg s 1 Ò, apple ŒÊapple Ÿ ªÁà UÃÊ Ò ÿ ÁŸ Êÿ œë appleu-œë appleu ŸË Ê ÿáãã UÃÊ Ò ÁŸ Êÿ apple ŒÊapple Ÿ Ë ÿê ÁòÊ Ê Êapple apple Ê UÁê ÊŸ apple ÊœÊ ÊappleŸapple apple ªŸapple flê apple ÿ Ê ÁŸ Uà ʟ ÊappleªÊ s 3.5 s 5 s 7 s 9 IX - PHYSICS
13. A standing wave is formed by the superposition of two waves travelling in opposite directions. The transverse displacement is given by 5 yx (, t) 0.5 sin π = x cos(00 πt). 4 What is the speed of the travelling wave moving in the positive x direction? (x and t are in meter and second, respectively.) 160 m/s 90 m/s 180 m/s 10 m/s 13. ŒÊapple à Uªapple, Êapple Áfl UËà ÁŒ ÊÊ apple ø U Ë Ò, apple äÿê UÊapple áê apple ªÊ Ë Ã Uª ŸÃË Ò Á Ê ŸÈ SÕ ÁflSÕÊ Ÿ ÁŸêŸ Ë UáÊ mê UÊ Á πê Ê ÃÊ Ò 5 yx (, t) 0.5 sin π = x cos(00 πt). 4 +x ˇÊ Ë Ã U» ø Ÿapple flê Ë ªÊ Ë Ã Uª Ë ªÁà ÊappleªË (ÿ Ê x fl t Ê Ë U U fl apple á«u apple Ò ) 160 m/s 90 m/s 180 m/s 10 m/s 10 IX - PHYSICS
14. Four closed surfaces and corresponding charge distributions are shown below. 14. øê U Œ Îc U ÃÕÊ Ÿ apple Êflapple Ê ÁflãÿÊ Êapple ÁŸêŸ ÁøòÊ apple Œ ÊÊ ÿê ªÿÊ Ò Let the respective electric fluxes through the surfaces be Φ 1, Φ, Φ 3 and Φ 4. Then : Φ 1 < Φ =Φ 3 > Φ 4 Φ 1 > Φ > Φ 3 > Φ 4 Φ 1 =Φ =Φ 3 =Φ 4 Φ 1 > Φ 3 ; Φ < Φ 4 ÿᜠŸ apple Îc U apple h flòlèã ç Ä Ê Φ 1, Φ, Φ 3 ÃÕÊ Φ 4 Êapple ÃÊapple Φ 1 < Φ =Φ 3 > Φ 4 Φ 1 > Φ > Φ 3 > Φ 4 Φ 1 =Φ =Φ 3 =Φ 4 Φ 1 > Φ 3 ; Φ < Φ 4 11 IX - PHYSICS
15. A combination of parallel plate capacitors is maintained at a certain potential difference. 15. Êãà U å apple U œêá UòÊÊapple apple ÿêapple Ÿ Êapple ÁŸÁ øã Áfl flêãã U U UπÊ ªÿÊ Ò (ÁøòÊ ŒappleÁπÿapple) When a 3 mm thick slab is introduced between all the plates, in order to maintain the same potential difference, the distance between the plates is increased by.4 mm. Find the dielectric constant of the slab. 3 4 5 6 16. A uniform wire of length l and radius r has a resistance of 100 Ω. It is recast into a wire of radius r. The resistance of new wire will be : 1600 Ω 400 Ω 00 Ω 100 Ω 3 mm Êapple appleu ªÈ U apple Êapple Ë œêá UòÊÊapple Ë å apple UÊapple apple Ëø «UÊ Ê ÊÃÊ Ò, ÃÊapple fl Ë Áfl flêãã U ŸÊÿapple UπŸapple apple Á å apple UÊapple apple Ëø Ë ŒÍ UË Êapple.4 mm apple ÊŸÊ «ÃÊ Ò ªÈ U apple Ê UÊflÒlÈÃÊ ÊappleªÊ 3 4 5 6 16. ê Êß l ÃÕÊ ÁòÊíÿÊ r apple ÊŸ ÃÊ U Ê Áà UÊappleœ 100 Ω Ò ß Êapple ÁòÊíÿÊ r apple ÃÊ U apple ÈŸ UÊ Ê ÊÃÊ Ò Ÿÿapple ÃÊ U Ê Áà UÊappleœ ÊappleªÊ 1600 Ω 400 Ω 00 Ω 100 Ω 1 IX - PHYSICS
17. The figure shows three circuits I, II and III which are connected to a 3V battery. If the powers dissipated by the configurations I, II and III are P 1, P and P 3 respectively, then : 17. ÁŒÿapple ªÿapple ÁøòÊ apple ÃËŸ Á U Õ, I, II fl III Êapple 3V Ò U UË apple Êapple«Ê ªÿÊ Ò ÿᜠÁflãÿÊ I, II ÃÕÊ III Ê P 1, P ÃÕÊ P 3 ÊÁÄà ÿÿ UÃapple Ò ÃÊapple P 1 > P > P 3 P 1 > P > P 3 P 1 > P 3 > P P > P 1 > P 3 P 3 > P > P 1 18. A negative test charge is moving near a long straight wire carrying a current. The force acting on the test charge is parallel to the direction of the current. The motion of the charge is : away from the wire towards the wire parallel to the wire along the current parallel to the wire opposite to the current P 1 > P 3 > P P > P 1 > P 3 P 3 > P > P 1 18. áêêà UˡÊáÊ Êflapple Ê, Ëœapple ê apple ÃÊ U, Á apple œê UÊ U Ë Ò, apple ÁŸ U ø U Ê Ò UˡÊáÊ Êflapple Ê U ªŸapple flê Ê œê UÊ Ë ÁŒ ÊÊ apple Êãà U Ò Êflapple Ê Ë ªÁà ÊappleªË ÃÊ U apple ŒÍ U ÃÊ U Ë Êapple U ÃÊ U apple Êãà U fl œê UÊ Ë ÁŒ ÊÊ apple ÃÊ U apple Êãà U fl œê UÊ Ë Áfl UËà ÁŒ ÊÊ apple 13 IX - PHYSICS
19. A uniform magnetic field B of 0.3 T is along the positive Z-direction. A rectangular loop (abcd) of sides 10 cm 5 cm carries a current I of 1 A. Out of the following different orientations which one corresponds to stable equilibrium? 19. 0.3 T Ê ÊŸ øèê Ëÿ ˇÊappleòÊ B œÿêà Z- ˇÊ Ë Ã U» ÁŒÁ ÊÃ Ò 10 cm ÃÕÊ 5 cm È Ê Êapple flê apple ÊÿÃÊ Ê U Ê Ê (abcd) apple 1 A œê UÊ I ÃË Ò ÁŸêŸ apple apple ÊÒŸ- Ê ÁŒª ÁflãÿÊ ÁSÕ U ÊêÿÊflSÕÊ Êapple ŒÁ Ê Ã UÃÊ Ò? 14 IX - PHYSICS
0. A sinusoidal voltage of peak value 83 V and angular frequency 30/s is applied to a series LCR circuit. Given that R=5 Ω, L=5 mh and C=1000 µf. The total impedance, and phase difference between the voltage across the source and the current will respectively be : 0. 83 V ûê Áfl fl ÃÕÊ 30 s 1 ÊappleáÊËÿ ÊflÎÁûÊ flê apple íÿêfl Ëÿ Áfl fl Êapple üêappleáêë LCR Á U Õ apple ªÊÿÊ ªÿÊ Ò ÁŒÿÊ Ò R=5 Ω, L=5 mh ÊÒ U C=1000 µf Á U Õ Ë È ÁÃ ÊœÊ ÃÕÊ dêappleã Áfl fl fl œê UÊ apple Ëø Ê Ã U Ê ÊappleªÊ 1 5 10 Ω and tan 3 7 Ω and 45 10 Ω ÊÒ U 1 5 tan 3 10 Ω and 7 Ω and 1 8 tan 3 1 5 tan 3 1. The electric field component of a monochromatic radiation is given by E = E 0 i cos k z cos ωt Its magnetic field B is then given by : E 0 c E 0 c E 0 c E 0 c j sin k z cos ωt j sin k z sin ωt j sin k z sin ωt j cos k z cos ωt 7 Ω ÊÒ U 45 10 Ω ÊÒ U 7 Ω ÊÒ U 1 8 tan 3 1 5 tan 3 1. Á Ë fláêë ÿ ÁflÁ UáÊ apple flòlèã ˇÊappleòÊ ÉÊ U Êapple ÁŸêŸ Ê U apple ÿäã Á ÿê Ê ÃÊ Ò E = E 0 i cos k z cos ωt apple øèê Ëÿ ˇÊappleòÊ B Ê ÊŸ ÊappleªÊ E 0 c E 0 c E 0 c E 0 c j sin k z cos ωt j sin k z sin ωt j sin k z sin ωt j cos k z cos ωt 15 IX - PHYSICS
. In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 0 cm from the lens. The focal length of the convex mirror is : 7.5 cm 0.0 cm 5.0 cm 30.5 cm 3. A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength 6000 Å and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band from the central bright band is : 3 mm 9 mm 4.5 mm 1.5 mm 4. A Laser light of wavelength 660 nm is used to weld Retina detachment. If a Laser pulse of width 60 ms and power 0.5 kw is used the approximate number of photons in the pulse are : [Take Planck s constant h=6.6 10 34 Js] 10 0 10 18 10 10 19. ÿêappleª apple ŒÊÒ UÊŸ, 15 cm» Êapple ŒÍ UË apple ûê apple Êapple Ê Ê apple ø U ûê Œ áê apple Ê Ÿapple 5 cm ŒÍ UË U ÊˇÊËÿ ÁSÕÁà apple UπÊ ªÿÊ Ò ÿᜠflsãè Êapple apple apple 0 cm Ë ŒÍ UË U UπÊ Êÿapple ÃÊapple flsãè ÃÕÊ Ê ÁÃÁ ê ÊÃË Êapple ÊÃapple Ò ûê Œ áê Ë» Êapple ŒÍ UË ÊappleªË 7.5 cm 0.0 cm 5.0 cm 30.5 cm 3. 0.1 mm øêò«êß Ë Á Ê UË 6000 Å Ã UªŒÒÉÿ apple Êãà U Á UáÊ È apple ÊÁ ÊÃ Ë ÊÃË Ò ÊÒ U Áflflà Ÿ Òá«U Êapple Á Ê UË apple 0.5 m ŒÍ U ÁSÕà Œapple U ŒappleπÊ ÊÃÊ Ò ÃÎÃËÿ ŒËåà Òá«U Ë apple 㜠Ëÿ ŒËåà Òá«U apple ŒÍ UË ÊappleªË 3 mm 9 mm 4.5 mm 1.5 mm 4. 660 nm à UªŒÒÉÿ Ë apple$ U Êß U Êapple appleuá UŸÊ ÁflÿÊapple Ÿ Êapple Êapple«Ÿapple apple Á ÿêappleª Á ÿê ÊÃÊ Ò ÿᜠ60 ms øêò«êß fl 0.5 kw ÊÁÄà apple apple$ U S 㜠(pulse) Ê ÿêappleª Á ÿê Êÿapple ÃÊapple S 㜠apple» Êapple UÊÚŸÊapple Ë ÅÿÊ ª ª ÊappleªË [å Ê ÁŸÿÃÊ h=6.6 10 34 Js] 10 0 10 18 10 10 19 16 IX - PHYSICS
5. The acceleration of an electron in the first orbit of the hydrogen atom (n=1) is : h 3 π m r h 3 8π m r h 3 4π m r h 3 4πm r 6. Imagine that a reactor converts all given mass into energy and that it operates at a power level of 10 9 watt. The mass of the fuel consumed per hour in the reactor will be : (velocity of light, c is 3 10 8 m/s) 0.96 gm 0.8 gm 4 10 gm 6.6 10 5 gm 7. The current gain of a common emitter amplifier is 69. If the emitter current is 7.0 ma, collector current is : 9.6 ma 6.9 ma 0.69 ma 69 ma 5. Êß«UÊapple Ÿ U ÊáÊÈ Ë Õ ˇÊÊ (n=1) apple ß appleä UÊÚŸ Ê àfl UáÊ ÊappleªÊ h 3 π m r h 3 8π m r h 3 4π m r h 3 4πm r 6. À ŸÊ ËÁ, U UË, ÊappleÁ ÁŒÿapple ªÿapple ÍáÊ Œ ÿ ÊŸ Êapple Ê apple Œ ÃË Ò fl 10 9 watt Ë ÊÁÄà Sà U U ø ÃË Ò UË apple ÉÊá appleu apple π à ÊappleŸapple flê apple ßZœŸ Ê Œ ÿ ÊŸ ÊappleªÊ ( Ê Ê Ê flappleª, c=3 10 8 m/s) 0.96 gm 0.8 gm 4 10 gm 6.6 10 5 gm 7. ÿáÿc U à flœ Ê œê UÊ Ê 69 Ò ÿáœ à œê UÊ Ê ÊŸ 7.0 ma Êapple ÃÊapple ª Ê œê UÊ Ê ÊŸ ÊappleªÊ 9.6 ma 6.9 ma 0.69 ma 69 ma 17 IX - PHYSICS
8. A signal is to be transmitted through a wave of wavelength λ, using a linear antenna. The length l of the antenna and effective power radiated P eff will be given respectively as : (K is a constant of proportionality) l λ, P eff = K λ λ l, P eff = K 8 λ λ 16 3 l, P eff = K λ λ l, P eff = K 5 λ 1 8. à UªŒÒÉÿ λ Ë Ã Uª mê UÊ Œapple Ê Êapple appleuπëÿ ã appleuÿê apple ÊÁ Uà UŸÊ Ò ã appleuÿê Ë ê Êß l ÃÕÊ ÊflË à Á à ÊÁÄà P eff Ê Ê ÊŸ ÊappleªÊ (K ÊŸÈ ÊÁà ÁSÕ UÊ (constant of proportionality) Ò) l λ, P eff = K λ λ l, P eff = K 8 λ 3 λ l, P eff = K 16 λ λ l, P eff = K 5 λ 1 18 IX - PHYSICS
9. In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance P=4 Ω and the neutral point N is at 60 cm from A. Now an unknown resistance R is connected in series to P and the new position of the neutral point is at 80 cm from A. The value of unknown resistance R is : 9. Á Ë Ë U U appleãè ÿêappleª apple ŒÊÒ UÊŸ, Áà UÊappleœÊapple Êapple ÁøòÊÊŸÈ Ê U Êapple«Ê ªÿÊ Ò ÊÈM apple Áà UÊappleœ P=4 Ω ÃÕÊ Ÿ Á ãœè N, Á ãœè A apple, 60 cm Ë ŒÍ UË U Ò ôêêã Áà UÊappleœ R Êapple P apple ÊÕ üêappleáêë apple Êapple«Ê ÊÃÊ Ò Á apple Ÿ Á ãœè Ë Ÿß ÁSÕÁà Á ŒÈ A apple 80 cm ŒÍ U Êapple ÊÃË Ò ôêêã Áà UÊappleœ R Ê ÊŸ ÊappleªÊ 33 5 Ω 6 Ω 7 Ω 0 3 Ω 33 5 Ω 6 Ω 7 Ω 0 3 Ω 19 IX - PHYSICS
30. In an experiment to determine the period of a simple pendulum of length 1 m, it is attached to different spherical bobs of radii r 1 and r. The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5 10 4 s, the difference in radii, r 1 r is best given by : 1 cm 0.1 cm 0.5 cm 0.01 cm - o 0 o - 30. ÿêappleª apple, 1 m ê Êß Ë U ŒÊapple Ê ÊflÃ Ê ÁŸ Ê Ÿapple appleãè Êapple r 1 ÃÕÊ r ÁòÊíÿÊ Êapple apple ª- ª ªÊapple Ê Ê U Êapple apple Êapple«Ê ÊÃÊ Ò ŒÊappleŸÊapple ªÊapple Ê Ê U Êapple Êapple apple Œ ÿ ÊŸ Áflà UáÊ ÊŸ Ò ÿᜠÊflÃ Ê Êapple Ê Ê appleˇê à U 5 10 4 s ÊÿÊ ªÿÊ Êapple ÃÊapple Ÿ Ë ÁòÊíÿÊ Êapple apple ãã U, r 1 r Ê ÁŸ Uà ʟ ÊappleªÊ 1 cm 0.1 cm 0.5 cm 0.01 cm - o 0 o - 0 IX - PHYSICS