( ) PART C PHYSICS. Sol. (2) Charge on the capacitor at any time t is. at t = 2τ

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1 JEE (MAN)-3-CMP -8 PAT C PHYSCS 6. n an C circuit as shown below both switches are open initially. Now switch S is closed, S kept open. (q is charge on the capacitor and τ C is capacitive time constant). Which of the following statement is correct? S C S At t τ, q C/ () At t τ, q C( e ) τ At t, q C( e ) Work done by the battery is half of the energy dissipated in the resistor. Sol. () Charge on the capacitor at any time t is t/ ( ) q C e τ at t τ q C( e ) 6. A diode detector is used to detect an amplitude modulated wave of 6% modulation by using a condenser of capacity 5 pico farad in parallel with a load resistance kilo ohm. Find the maximum modulated frequency which could be detected by it..6 khz () 5.3 MHz 5.3 khz.6 MHz Sol. fc 6.37 khz π C f C cut off frequency As we know that f m f C is correct Note: The maximum frequency of modulation must be less than f m, where m fm fc m m modulation index 63. The supply voltage to a room is. The resistance of the lead wires is 6 Ω. A 6 W bulb is already switched on. What is the decrease of voltage across the bulb, when a 4 W heater is switched on in parallel to the bulb?.9 olt () 3.3 olt.4 olt zero volt Sol. esistance of bulb 4Ω 6 esistance of Heater 6Ω 4 6 Ω Heater Bulb FTJEE td., FTJEE House, 9-A, Kalu Sarai, Sarvapriya ihar, New Delhi -6, Ph 466, , Fax 65394

2 JEE (MAN)-3-CMP-9 oltage across bulb before heater is switched on, 4 46 oltage across bulb after heater is switched on, Decrease in the voltage is.4 (approximately) Note: Here supply voltage is taken as rated voltage. 64. A uniform cylinder of length and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density σ at equilibrium position. The extension x of the spring when it is in equilibrium is: Mg Aσ Mg Aσ () k M k M Mg Aσ + Mg k M k (Here k is spring constant) Sol. () At equilibrium ΣF A kx + σg Mg Aσ x Mg M kx Mg Buoyant force 65. Two charges, each equal to q, are kept at x a and x a on the x-axis. A particle of mass m and charge q q is placed at the origin. f charge q is given a small displacement (y a) along the y-axis, the net force acting on the particle is proportional to: y () y y y Sol. F net Fcosθ k q q / y ( ) a + y a + y kq y (y a) 3 a q F a θ θ q/ y a F q 66. A beam of unpolarised light of intensity is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane makes an angle of 45 relative to that of A. The intensity of the emergent light is: / () /4 /8 Sol. () 67. The anode voltage of a photocell is kept fixed. The wavelength λ of the light falling on the cathode is gradually changed. The plate current of the photocell varies as follows: FTJEE td., FTJEE House, 9-A, Kalu Sarai, Sarvapriya ihar, New Delhi -6, Ph 466, , Fax 65394

3 JEE (MAN)-3-CMP - () λ λ λ λ Sol. 68. Two coherent point sources S and S are separated by a small distance d as shown. The fringes obtained on the screen will be: straight lines () semi-circles concentric circles points S d S D Screen Sol. 69. A metallic rod of length l is tied to a string of length l and made to rotate with angular speed ω on a horizontal table with one end of the string fixed. f there is a vertical magnetic field B in the region, the e.m.f. induced across the ends of the rod is: 3Bωl 5Bωl () 4Bωl Bωl Sol. de B( ωx) dx 3 e B xdx ω 5Bω x ω 7. n a hydrogen like atom electron makes transition from an energy level with quantum number n to another with quantum number (n ). f n >>, the frequency of radiation emitted is proportional to () 3/ n n 3 n n Sol. ν (n ) n (n ) n (n ) (since n ) 3 n FTJEE td., FTJEE House, 9-A, Kalu Sarai, Sarvapriya ihar, New Delhi -6, Ph 466, , Fax 65394

4 JEE (MAN)-3-CMP- 7. Assume that a drop of liquid evaporates by decrease in its surface energy, so that its temperature remains unchanged. What should be the minimum radius of the drop for this to be possible? The surface tension is T, density of liquid is ρ and is its latent heat of vaporization. T / ρ () T/ρ T/ρ ρ/t Sol. ρ4π T 4π[ ( - ) ] ρ T[ + - ] ρ T ( is very small) T ρ. 7. The graph between angle of deviation (δ) and angle of incidence (i) for a triangular prism is represented by: δ () δ i i δ δ Sol. () i i 73. et [ε ] denote the dimensional formula of the permittivity of vacuum. f M mass, length, T time and A electric current, then: [ε ] [M - -3 T 4 A ] () [ε ] [M - T - A - ] [ε ] [M - T - A] [ε ] [M - -3 T A] Sol. 73. q 4πε r F [A T ] 3 4 ε [M A T ] [MT ] 74. p A B p p D C v v v The above p-v diagram represents the thermodynamic cycle of an engine, operating with an ideal monoatomic gas. The amount of heat extracted from the source in a single cycle is 3 p v () p v 4p v p v Sol. () Heat is extracted from the source in path DA and AB is FTJEE td., FTJEE House, 9-A, Kalu Sarai, Sarvapriya ihar, New Delhi -6, Ph 466, , Fax 65394

5 JEE (MAN)-3-CMP - 3 P 5 P Q + 3 P 75. A sonometer wire of length.5 m is made of steel. The tension in it produces an elastic strain of %. What is the fundamental frequency of steel if density and elasticity of steel are kg/m 3 and. N/m respectively? 78. Hz ().5 Hz 77 Hz 88.5 Hz Sol. Fundamental frequency f T l µ T l Aρ stress. 3 l ρ This question has statement and statement. f the four choices given after the statements, choose the one that best describes the two statements. Statement- : Higher the range, greater is the resistance of ammeter. Statement- : To increase the range of ammeter, additional shunt needs to be used across it. Statement is true, Statement is true, Statement is not the correct explanation of Statement. () Statement is true, statement is false. Statement is false, Statement is true Statement is true, Statement is true, Statement is the correct explanation of statement-. Sol. For Ammeter, S G g g So for to increase, S should decrease, so additional S can be connected across it. 77. What is the minimum energy required to launch a satellite of mass m from the surface of a planet of mass M and radius in a circular orbit at an altitude of? GmM () GmM 3 Sol. GmM 3 T. E f GMm 6 T. E i GMm W T.E f T.E i 5GMm A projectile is given an initial velocity of ( iˆ + ˆ) vertical. f g m/s, the equation of its trajectory is: Sol. y x 5x () 4y x 5x 5GmM 6 j m/s, where î is along the ground and ĵ is along the 4y x 5x y x 5x FTJEE td., FTJEE House, 9-A, Kalu Sarai, Sarvapriya ihar, New Delhi -6, Ph 466, , Fax 65394

6 JEE (MAN)-3-CMP-3 x t y t 5t Equation of trajectory is y x 5x 79. Two capacitors C and C are charged to and respectively. t is found that by connecting them together the potential on each one can be made zero. Then : 3C 5C () 3C + 5C 9C 4C 5C 3C Sol. C C 6C C 3C 5C 8. A hoop of radius r and mass m rotating with an angular velocity ω is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip? rω 3 () rω Sol. () From conservation of angular momentum about any fix point on the surface mr ω mr ω ω CM ω r ω 8. An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is and its pressure is P. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency: MP π A γ M π Aγ P () rω rω 4 π A γ P M Aγ P π M Sol. () P atm A P A mg FBD of piston at equilibrium P atm A + mg P A... P atm A mg (P + dp) A FBD of piston when piston is pushed down a distance x FTJEE td., FTJEE House, 9-A, Kalu Sarai, Sarvapriya ihar, New Delhi -6, Ph 466, , Fax 65394

7 JEE (MAN)-3-CMP -4 d x P atm + mg (P +dp) A m...() dt Process is adiabatic P γ γ C dp Pd Using,, 3 me get f π A γ P M 8. A charge Q is uniformly distributed over a long rod AB of length as shown in the figure. The electric potential at the point lying at a distance from the end A is: A B 3Q Q () 4πε 4πε ln Sol. Q ln 4πε Q 8πε x dx ln x k Q Q x dx x 4πε 83. A circular loop of radius.3 cm lies parallel to a much bigger circular loop of radius cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 5 cm. f a current of. A flows through the smaller loop, then the flux linked with bigger loop is 6 weber () 3.3 weber weber 9. weber Sol. r d et M be the coefficient of mutual induction between loops φ M i M i 3/ µ ( d + ) π r µ π r 3/ ( d + ) M i φ Mi φ 9. weber 84. f a piece of metal is heated to temperature θ and then allowed to cool in a room which is at temperature θ the graph between the temperature T of the metal and time t will be closest to : T () T θ θ t t FTJEE td., FTJEE House, 9-A, Kalu Sarai, Sarvapriya ihar, New Delhi -6, Ph 466, , Fax 65394

8 JEE (MAN)-3-CMP-5 T T θ t t Sol. () The temperature goes on decreasing with time (non-linearly) The rate of decrease will be more initially which is depicted in the second graph. 85. The characteristic of an ED is B G Y () Y G B ed Yellow Green Blue ()(Y)(G)(B) Sol. For ED, in forward bias, intensity increases with voltage. 86. This question has Statement and Statement. f the four choices given after the Statements, choose the one that best describes the two Statements. Statement : A point particle of mass m moving with speed v collides with stationary point particle of m mass M. f the maximum energy loss possible is given as f mv then f M + m. Statement : Maximum energy loss occurs when the particles get stuck together as a result of the collision. Statement is true, Statement is true, Statement is not a correct explanation of Statement. () Statement is true, Statement is false. Statement is false, Statement is true Statement is true, Statement is true, Statement is a correct explanation of Statement. Sol. oss of energy is maximum when collision is inelastic as in an inelastic collision there will be maximum deformation. Mm KE in CM frame is M + m rel Mm KE i KE f ( Q rel ) M + m Mm Hence loss in energy is M + m M f M + m FTJEE td., FTJEE House, 9-A, Kalu Sarai, Sarvapriya ihar, New Delhi -6, Ph 466, , Fax 65394

9 JEE (MAN)-3-CMP The amplitude of a damped oscillator decreases to.9 times its original magnitude is 5s. n another s it will decrease to α times its original magnitude, where α equals..8 () Sol. () A A e kt 5k.9A A e 5k and α A A e solving α Diameter of plano-convex lens is 6 cm and thickness at the centre is 3 mm. f speed of light in material of lens is 8 m/s, the focal length of the lens is : cm () 3 cm cm 5 cm Sol. () -t d t d + ( t ) t d d t 9 5 cm ( 3) 6 ( µ ) f 3 f 5 f 3 cm 89. The magnetic field in a travelling electromagnetic wave has a peak value of nt. The peak value of electric field strength is : 6 /m () 9 /m /m 3 /m Sol. Ε CB /m 9. Two short bar magnets of length cm each have magnetic moments. Am and. Am respectively. They are placed on a horizontal table parallel to each other with their N poles pointing towards the South. They have a common magnetic equator and are separated by a distance of. cm. The value of the resultant horizontal magnetic induction at the mid - point of the line joining their centres is close to (Horizontal component of earth s magnetic induction is Wb/m ) FTJEE td., FTJEE House, 9-A, Kalu Sarai, Sarvapriya ihar, New Delhi -6, Ph 466, , Fax 65394

10 JEE (MAN)-3-CMP Wb/m () Wb/m Wb/m Wb/m Sol. B B + B + B net M M H µ M µ M 4 + B π x π x H µ ( M ) M + B π x H Wb/m FTJEE td., FTJEE House, 9-A, Kalu Sarai, Sarvapriya ihar, New Delhi -6, Ph 466, , Fax 65394

FIITJEE Solutions to AIEEE PHYSICS

FIITJEE Solutions to AIEEE PHYSICS FTJEE Solutions to AEEE - 7 -PHYSCS Physics Code-O 4. The displacement of an object attached to a spring and executing simple harmonic motion is given by x = cos πt metres. The time at which the maximum