Prerna Tower, Road No 2, Contractors Area, Bistupur, Jamshedpur , Tel (0657) , PART A PHYSICS

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1 R Prerna ower, Road No, Contractors Area, Bistupur, Jamshedpur 8, el (657)89, AIEEE Physics PAR A PHYSICS. he transverse displacement y(x, t) of a wave on a string is given by y(x, t) = e [ax + bt + (ab) xt] his represents a : () Wave moving in x direction with speed (b / a) () Standing wave of frequency b () Standing wave of frequency ( / b) (4) Wave moving in +x direction with speed (a / b). () y(x, t) = e [ax + bt + (ab) xt] = e ( a x + b t) Coeff of x and t have same sign wave is moving in x direction v = (coeff of t / coeff of x) = (b / a). A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : mm Circular scale reading : 5 divisions Given that mm on main scale corresponds to divisions of the circular scale. he diameter of wire from the above data is : ().5 cm ().6 cm ().5 cm (4).5 cm. () LC = ( / ) mm Reading = + 5 =.5 mm=.5 cm. A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. he pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is: () g () ( / ) g () (g / ) (4) ( / ) g. () mg = ma... () and R = Iα R = (mr / ) (a / R) = (ma / )... () from () & () a = (g / ) AIEEE ( May ) Question & Solutions www. prernaclasses.com

2 4. Work done in increasing the size of a soap bubble from a radius of cm to 5 cm is nearly (Surface tension of soap solution =. Nm ) ().π mj () π mj ().4π mj (4) 4π mj 4. () W = U = S A =. 4π(5 9) 4.4 π mj 5. A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. he insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc: () continuously decreases () continuously increases () first increases and then decreases (4) remains unchanged 5. () Iω = constant As the insect moves towards the centre, I decreases ω increases. When the insect moves from centre to the rim, I increases ω decreases. 6. wo particles are executing simple harmonic motion of the same amplitude A and frequency ω along the x axis. heir mean position is separated by distance X (X > A). If the maximum separation between them is (X + A), the phase difference between their motion is: () (π / ) () (π / 4) () (π / 6) (4) (π / ) 6. () x = E.P E.P At maximum separation, relative velocity is zero particle at x = ( A / ) moving along +ve x direction and particle at x = [X + (A / )] moving along +ve x direction. Phase for particle = ( π / 6) and phase for particle = (+π / 6) φ = (π / ) 7. wo bodies of masses m and 4m are placed at a distance r. he gravitational potential at a point on the line joining them where the gravitational field is zero is: () (4Gm / r) () (6Gm / r) () (9Gm / r) (4) Zero 7. () m x p r 4m Field to be zero,(gm / x ) = [g(4m) / (r x) ] x = (r / ) So potential at p = Gm G ( 4 m ) = ( GM / r) ( + 6) = ( 9Gm / r) r r AIEEE ( May ) Question & Solutions www. prernaclasses.com

3 8. wo identical charged spheres suspended from a common point by two massless strings of length L are initially a distance d(d << L)apart because of their mutual repulsion. he charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. hen as a function of distance x between them, () v x () v x / () v x (4) v x / 8. (4) F = (kq / x ) mg (x / L) q = cx.5. dq / dt =.5c x v. Since dq / dt = constant, v x /. 9. A boat is moving due east in a region where the earth s magnetic field is 5. 5 NA m due north and horizontal. he boat carries a vertical aerial m long. If the speed of the boat is.5 ms, the magnitude of the induced emf in the wire of aerial is: ().75 mv ().5 mv ().5 mv (4) mv 9. () ε = =.5 mv. An object, moving with a speed of 6.5 ms, is decelerated at a rate given by: (dv / dt) =.5 v where v is the instantaneous speed. he time taken by the object, to come to rest, would be: () s () 4 s () 8 s (4) s. () (dv / dt) =.5 v (dv / v) =.5 dt dv = dt v t = (.5) /.5) = sec. 5 [ v ] =.5 t 6.5. A fully charged capacitor C with initial charge q is connected to a coil of self inductance L at t =. he time at which the energy is stored equally between the electric and the magnetic fields is: () (π / 4) LC () π LC () LC (4) π LC. () for L.C oscillation.p = π (LC). ime at which energy will be equal = (.P / 8) = [π (LC) / 8] = (π / 4) (LC). Let the x z plane be the boundary between two transparent media. Medium in z has a refractive index of and medium with z < has a refractive index of. A ray of light in r medium given by the vector A = 6 i ˆ + 8 j ˆ k ˆ is incident on the plane of separation. he angle of refraction in medium is: () 45 () 6 () 75 (4). () Note : In question plane should be x y not x z. As boundary Angle made with z axis, cos θ = ( / ) = ( / ) θ = 6 Using Snell s law,. sin 6 =. sin r sin r = ( / ) r = 45. AIEEE ( May ) Question & Solutions www. prernaclasses.com

4 . A current I flows in an infinitely long wire with cross section in the form of a semi circular ring of radius R. he magnitude of the magnetic induction along its axis is: () (µ I / π R) () (µ I / πr) () (µ I / 4πR) (4) (µ I / π R) Rdθ db dq C edθ. (4) A θ θ o θ B db µ I Resultant B will be along AB. db' = db cos θ= Rd θ cos θ π R π R π / µ I db ' = θ θ π cos d R µ I ' = π R B 4. A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats γ. It is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by: () [(γ ) / γr]mv K () [γmv / R]K () [(γ ) / R]Mv K (4) [(γ ) / (γ + )R]Mv K 4. () K.E = ( / ) (n. M) V = n. (R / (γ )). = [((γ ) MV ) / R] 5. A mass M, attached to a horizontal spring executes S.H.M. with amplitude A. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A. he ratio of (A / A ) is: () [(M + m) / M] () [M / (M + m)] / () [(M + m) / M] / (4) [M / (M + m)] 5. () When only M mass attached with spring. hen ( / ) K A = ( / ) MV V = (K / M). A () using C.L.M MV = (m + M)V V = (M / (m + M)) V () for (m + M) mass with spring : ( / ) KA = ( / ) (m + M) V V = (K / (m + M)) A () for (), () and () (K / (m + M)) A = M / (m + M). (K / M). A (A / A ) = ((M + m) / M) / AIEEE ( May ) Question & Solutions 4 www. prernaclasses.com

5 6. Water is flowing continuously from a tap having an internal diameter 8 m. he water velocity as it leaves the tap is.4 ms. he diameter of the water stream at a distance m below the tap is close to: () 7.5 m () 9.6 m ().6 m (4) 5. m 6. () V = (V + gh) = ((.4) + ) = (4.6) ms By continuity, A V = A V d V = d V d = d (V / V ) = m 7. his question has Statement and Statement. Of the four choices given after the statements, choose the one that best describes the two statements. Statement : Sky wave signals are used for long distance radio communication. hese signals are in general, less stable than ground wave signals. Statement : he state of ionosphere varies from hour to hour, day to day and season to season. () Statement is true, Statement is true, Statement is the correct explanation of Statement. () Statement is true, Statement is true, Statement is not the correct explanation of Statement. () Statement is false, Statement is true. (4) Statement is true, Statement is false. 7. () 8. hree perfect gases at absolute temperatures and and are mixed. the masses of molecules are m, m and m and the number of molecules are n, n and n respectively. Assuming no loss of energy, the final temperature of the mixture is : () () n + n + n n + n + n n + n n + n + n + n () (4) n + n + n n + n ( + + ) + n 8. () Note : It needs to be asssumed that all the three gases have the same atomicity. Σ ( / ) n i. ( / ) k i = (n + n + n ) [( / ) k)] (internal energy constant) = [(n + n + n ) / (n + n + n )] AIEEE ( May ) Question & Solutions 5 www. prernaclasses.com

6 9. A pulley of radius m is rotated about its axis by a force F = ( t 5 t ) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is kg m, the number of rotations made by the pulley before its direction of motion if reversed, is : () more than but less than 6 () more than 6 but less than 9 () more than 9 (4) less than 9. () α = (FR / I) = [(t 5t ) / ] = 4t t t ω = α dt = [t (t / )] ω = t = 6 sec θ = 6 ω dt = 6 rad. Rotations = 6 / π which is slightly less than 6.. A resistor R and µf capacitor in series is connected through a switch to V direct supply. Across the capacitor is a neon bulb that light up at V. Calculate the value of R to make the bulb light up 5 s after the switch has been closed (log.5 =.4) ().7 5 Ω ().7 6 Ω (). 7 Ω (4). 4 Ω. () q = CE ( e t / RC ) V = (q / C) = E ( e t / RC ) V = V at t = 5 sec = (( e 5 / R 6 ) R.7 6 Ω. A Carnot engine operating between temperatures and has efficiency ( / 6). When is lowered by 6 K, its efficiency increases to ( / ). hen and are, respectively : () 7 K and K () K and 68 K () K and 48 K (4) 7 K and K. (4) > η = [ ( / )] (5 / 6) = ( / ) Also ( / ) = [ / 6) / ]. (6 / 5) = = [ ( / 5) ] [(5 86) / ] = = K. If a wire is stretched to make it.% longer, its resistance will : () increase by. % () decrease by. % () decrease by.5 % (4) increase by.5 %. () R = (ρl / A), Volume = LA = constant L / L = ( A / A) ( R / R) = ( L / L) ( A / A)] = ( L / L) =.% AIEEE ( May ) Question & Solutions 6 www. prernaclasses.com

7 . Direction : he question has paragraph followed by two statements, Statement and Statement. Of the given four alternatives after the statements, choose the one that describes the statements.. () A thin air film is formed by putting the convex surface of a plane convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film. Statement : When light reflects from the air glass plate interface, the reflected wave suffers a phase change of π. Statement : he centre of the interference pattern is dark. () Statement is true, Statement is true and Statement is the correct explanation of statement () Statement is true, Statement is true and Statement is not the correct explanation of Statement () Statement is false, Statement is true (4) Statement is true, Statement is false 4. A car is fitted with a convex side view mirror of focal length cm. A second car.8 m behind the first car is overtaking the first car at a relative speed of 5 ms. he speed of the image of the second car as seen in the mirror of the first one is : () ms () ms 5 () 5 ms (4) ms 4. () [( / v) + ( / u)] = ( / f) ( / v ) v im + ( / u )v m = v im = (v / u )v m v im = (v / u) v m [( / v) + ( / 8)] = ( / ) ( / v) = [( / ) + ( / 8)] = (5 / 8) v = (8 / 5) v im = [8 / (5 8)] v m = (5 / 5) = ( / 5) ms 5. Energy required for the electron excitation in Li ++ from the first to the third Bohr orbit is : () 6. ev () 8.8 ev ().4 ev (4). ev 5. () E n = (.6 z / n )ev E = [+.6 9 ( ( / 9))] = = 8.8 ev 6. he electrostatic potential inside a charged spherical ball is given by φ = a r + b where r is the distance from the centre; a, b are constants. hen the charge density inside the ball is : () 6aε r () 4π aε () 6 aε (4) 4π aε r 6. () φ = ar + b E = (dφ / dr) = (d(ar + b) / dr) = ar flux = ( ar). 4πr = (q / ε ) q 8πar ε ρ = q / [(4 / )πr ] = 6 aε AIEEE ( May ) Question & Solutions 7 www. prernaclasses.com

8 7. A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is : 4 4 v π v () π () g g v () π (4) g 7. () area = πr max when R max = maximum horizontal range of water drops area = π [V sin 9 / g] = [πv 4 / g ] 8. g of water is heated from C to 5 C. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 484 J / kg / K) : () 8.4 kj () 84 kj (). kj (4) 4. kj 8. () Q = U + W W = (expansion is ignored) U = Q = m.s. θ = ( Kg) (484) (5 ) = 48.4 = 868 J = 8.4 KJ 9. he half life of a radioactive substance is minutes. he approximate time interval (t t ) between the time t when ( / ) of it has decayed and time t when ( / ) of it had decayed is : () 4 min () min () 8 min (4) 7 min 9. () t t = (. / λ) log [(N / ) / (N / )] = [(. ) /.69] log () = minutes. his question has Statement and Statement. Of the four choices given after statements, choose the one that best describes the two statements. Statement : A metallic surface is irradiated by a monochromatic light of frequency v > v (the threshold frequency). he maximum kinetic energy and the stopping potential are K max and V respectively. If the frequency incident on the surface is doubled, both the K max and V are also doubled. Statement : he maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light. () Statement is true, Statement is true, Statement is the correct explanation of Statement () Satement is true, Statement is true, Statement is not the correct explanation of Statement () Statement is false, Statement is true (4) Statement is true, Statement is false.. () hν = hν + K max () h(ν) = hν + K ' max () where K max is Kinetic energy after frequency is doubled K ' max = hν + K max [using () & ()] K ' max > K max ev ' > (ev ) where v ' is stopping potential after frequency is doubled v' > v Statement () is false statement () is true because K max = hν hν (linear equation) π v g AIEEE ( May ) Question & Solutions 8 www. prernaclasses.com