PHYSICS PAT II SECTION- I Straight objective Tpe This section contains 9 multiple choice questions numbered to 1. Each question has choices,, (C) and, out of which ONLY ONE is correct.. A parallel plate capacitor C with plates of unit area and separation d is filled with a liquid of dielectric constant K =. The level of liquid is d initiall. Suppose the liquid level decreases at a constant speed V, the time constant as a function of time t is C d d/ 6ε 5d + Vt (15d + 9 Vt) ε d dvt 9Vt (C) 6ε 5d Vt (15d 9 Vt) ε d + dvt 9Vt Sol. Ans [A] Let is thickness of dielectric ε A C = d + K Time constant = ε A d + K = ε 6ε = d Vt 5d + Vt d d + Vt. A light beam is travelling from egion I to egion IV (efer Figure). The refractive inde in egions I, II, III and IV are, n, n n and 6 n, 8 respectivel. The angle of incidence q for which the beam just misses entering egion IV is Amit Institute for Competitive Eaminations : Phones: 61/, 557111///, 951-189/ - 1 -
IIT-JEE-8 egion I egion II egion III egion IV θ n n 6 n 8. m.6 m sin 1 sin 8 1 1 (C) sin 1 1 sin 1 1 Sol. Ans [B] For parallel refracting surfaces µ sin i = constant n sin sin9 θ= n 8 θ= sin 8 1 1 5. A vibrating string of certain length l under a tension T resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length 75 cm inside a tube closed at one end. The string also generates beats per second when ecited along with a tuning fork of frequenc n. Now when the tension of the string is slightl increased the number of beats reduces to per second. Assuming the velocit of sound in air to be m/s, the frequenc n of the tuning fork in Hz is 6 (C) 117. 19. Sol. Ans [A] As tension increases, frequenc of vibrating string also increases. Given, for increase in tension, beat frequenc decreases. Frequenc of tuning fork = + = Hz.75 6. A radioactive simple S 1 having an activit of 5 µ Ci has twice the number of nuclei as another sample S which has an activit of 1 µ Ci. The half lifes of S 1 and S can be ears and 5 ears, respectivel ears and 1 ears, respectivel (C) 1 ears each 5 ears each Sol. Ans [A] 5 = λ 1 N 1 = λ N λ = 1 λ 1 or T1 T = Amit Institute for Competitive Eaminations : Phones: 61/, 557111///, 951-189/ - -
IIT-JEE-8 7. A transverse sinusoidal wave moves along a string in a positive -direction at a speed of 1 cm/s. The wavelength of the wave is.5 m and its amplitude is 1 cm. At a particular time t, the snap-shot of the wave is shown in figure. The velocit of point P when its displacement is 5 cm is P π ˆ π j m/s ˆ j m/s (C) 5 5 π ˆ π i m/s i ˆ m/s 5 5 Sol. Ans [A].5.1= T = 5sec. T ω= π 5 π v p = (1) (5) 1 = m/sec 5 5 Also particle velocit = wave velocit slope of wave form π Particle velocit, ( ) Slope at P is negative Particle velocit along positive ais. q q 8. Consider a sstem of three charges, and q placed at points A, B and C, respectivel, as shown in figure. Take O to be the centre of the circle of radius and angle CAB = 6º B C 6º O A q The electric field at point O is 8πε directed along the negative -ais The potential energ of the sstem is zero (C) The magnitude of the force between the charges at C and B is q The potential at point O is 1πε q 5πε Sol. Ans [B] V at O Kq/ Kq/ K( Kq /) = + + = Amit Institute for Competitive Eaminations : Phones: 61/, 557111///, 951-189/ - -
IIT-JEE-8 9. A block is attached to two unstretched springs S 1 and S with spring constants k and k, respectivel (see figure I). The other ends are attached to identical supports M 1 and M not attached to the walls. The springs and supports have negligible mass. There is no friction anwhere. The block B is displaced towards wall 1 b a small distance (figure II) and released. The block returns and moves a maimum distance towards wall. Displacements and are measured with respect to the equilibrium position of the block B. The ratio is M S S1 1 M1 I M S S1 1 M1 II (C) 1 1 Sol. Ans [C] 1 1 K( ) = K( ) 1 =. A glass tube of uniform internal radius (r) has a valve separating the two identical ends. Initiall, the valve is in a tightl closed position. End 1 has a hemispherical soap bubble of radius r. End has subhemispherical soap bubble as shown in figure. Just after opening the valve, 1 air from end 1 flows towards end. No change in the volume of the soap bubbles air from end 1 flows towards end. Volume of the soap bubble at end 1 decreases (C) no change occurs air from end flows towards end 1. Volume of the soap bubble at end 1 increases Sol. Ans [B] adius of bubble at 1 is less than radius of bubble at end (i.e. 1 < ) P = T Pressure inside bubble at 1 is more. Amit Institute for Competitive Eaminations : Phones: 61/, 557111///, 951-189/ - -
IIT-JEE-8 1. A bob of mass M is suspended b a massless string of length L. The horizontal velocit V at position A is just sufficient to make it reach the point B. The angle θ at which the speed of the bob is half of that at A, satisfies (C) Sol. Ans [D] π θ= π π <θ< π π <θ< π <θ<π 1 1 5g m( 5g) = mgh+ m Solving, 15 h= = 1.875 8 L A B θ V For π θ=, h= 1.77 θ> π SECTION- II ASSETION EASON TYPE This section contains multiple choice questions numbered to 5. Each question contains STATEMENT-1 (Assertion) and STATEMENT- (eason). Each question has choices,, (C) and out of which ONLY ONE is correct.. STATEMENT-1: For an observer looking out through the window of a fast moving train, the nearb objects appear to move in the opposite direction to the train, while the distant objects appear to the stationar. and STATEMENT-: If the observer and the object are moving at velocities V1and V respectivel with reference to a laborator frame, the velocit of the object with respect to the observer is V V1. Statement-1 is True, Statement- is True; Statement- is a correct eplanation for Statement-1 Statement-1 is True, Statement- is True; Statement- is NOT a correct eplanation for Statement-1 (C) Statement-1 is True, Statement- is False Statement-1 is False, Statement- is True Sol. Ans [B] Amit Institute for Competitive Eaminations : Phones: 61/, 557111///, 951-189/ - 5 -
IIT-JEE-8. STATEMENT-1: For particle purposes, the earth is used as a reference at zero potential in electrical circuits. and STATEMENT-: The electrical potential of a sphere of radius with charge Q uniforml distributed Q on the surface is given b. πε Statement-1 is True, Statement- is True; Statement- is a correct eplanation for Statement-1 Statement-1 is True, Statement- is True; Statement- is NOT a correct eplanation for Statement-1 (C) Statement-1 is True, Statement- is False Statement-1 is False, Statement- is True Sol. Ans [B] Charge on earth is ver large so small increment in charge does not change its potential. So potential of earth is taken to be positive.. STATEMENT-1: The sensitivit of a moving coil galvanometer is increased b placing a suitable magnetic material as a core inside the coil. and STATEMENT-: Soft iron has a high magnetic permeabilit and cannot be easil magnetized or demagnetized. Statement-1 is True, Statement- is True; Statement- is a correct eplanation for Statement-1 Statement-1 is True, Statement- is True; Statement- is NOT a correct eplanation for Statement-1 (C) Statement-1 is True, Statement- is False Statement-1 is False, Statement- is True Sol. Ans [C] Placing magnetic material increases magnetic material increases magnetic moment of coil, hence magnetic field associated with coil sensitivit θ NAB =. C C 5. STATEMENT-1 : It is easier to pull a heav object than to push it on a level ground. and STATEMENT-: The magnitude of frictional force depends on the nature of the two surfaces in contact. Statement-1 is True, Statement- is True; Statement- is a correct eplanation for Statement-1 Statement-1 is True, Statement- is True; Statement- is NOT a correct eplanation for Statement-1 (C) Statement-1 is True, Statement- is False Statement-1 is False, Statement- is True Amit Institute for Competitive Eaminations : Phones: 61/, 557111///, 951-189/ - 6 -
IIT-JEE-8 Sol. Ans [D] In case of pushing normal reaction between block and floor is more than that is in case of pulling and, f = µn. SECTION- III LINKED COMPEHENSION TYPE This section contains Paragraphs. Based upon each paragraph, multiple choice questions have to be answered. Each question has choices,, (C) and, out of which ONLY ONE is correct. Paragraph for Question Nos. 6 to 8 The nuclear charge (Ze) is non-uniforml distributed within a nucleus of radius. The charge densit ρ(r) [charge per unit volume] is dependent onl on the radial distance r from the centre of the nucleus as shown in figure. The electric field is onl along the radial direction. ρ( r) d a r 6. The electric field at r = is independent of a (C) directl proportional to a directl proportional to a inversel proportional to a Sol. Ans [A] Electric field at r = depends upon total charge enclosed. ze E. ds = ε E = πε ze i.e., it independent of a 7. For a =, the value of d (maimum value of ρ as shown in the figure) is Ze π Ze π Ze (C) π Ze π Sol. Ans [B] For a =, graph ρ(r) versus r is = + d d r d Amit Institute for Competitive Eaminations : Phones: 61/, 557111///, 951-189/ - 7 -
IIT-JEE-8 Total charge enclosed = ρ() r dv = π ze = d ze d = π d π r+ d r dr = 8. The electric field within the nucleus is generall observed to be linearl dependent on r. This implies πd a = a = (C) a = a = Sol. Ans [C] ρr Electric field varies linearl when charge densit is constant and for that, E =. ε Paragraph for Question Nos. 9 to 1 A uniform thin clindrical disk of mass M and radius is attached to two identical massless springs of spring constant k which are fied to the wall as shown in the figure. The springs are attached to the ale is massless and both the springs and the ale are in a horizontal plane. The unstretched length of each spring is L. The disk is initiall at its equilibrium position with its centre of mass (CM) at a distance L from the wall. The disk rolls without slipping with velocit V = Vi ˆ. The coefficient of friction is µ. Figure : d d d V 9. The net eternal force acting on the disk when its centre of mass is at displacement with respect to its equilibrium position is k k (C) k k Sol. Ans [D] 1 1 1 1 k + k + MV 1+ = constant Amit Institute for Competitive Eaminations : Phones: 61/, 557111///, 951-189/ - 8 -
Differentiating w.r.t. time d dv k + MV = dt dt dv k = dt M MdV dt = k. The centre of mass of the disk undergoes simple harmonic motion with angular frequenc ω equal to k M k M (C) k M k M Sol. Ans [D] k =ω M ω= k M 1. The maimum value of V for which the disk will roll without slipping is M µ g k M µ g (C) k M µ g k µ g 5M k Sol. Ans [C] For an displacement from the mean position. k f = k (from part I) f = k, for which friction is limiting. k =µ µ mg mg = For V to be maimum, this should be amplitude of SHM Now, conserving the mechanical energ, µ mg mv = ka = k m V =µ g k Amit Institute for Competitive Eaminations : Phones: 61/, 557111///, 951-189/ - 9 -
IIT-JEE-8 SECTION- IV MATIX-MATCH TYPE This section contains questions. Each question contains statements given in two columns which have to be matched. Statement (A, B, C, D) in Column I have to be matched with statements (p, q, r, s) in Column II.. Column I gives a list of possible set of parameters measured in some eperiments. The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters give in Column I with the graphs given in Column II. Indicate our answer b darkening the appropriate bubble of the matri given in the OS. Column I Potential energ of a simple pendulum ( ais) (p) Column II as a function of displacement (-ais) o Displacement ( ais) as a function of time (q) ( ais) for a one dimensional motion at zero or constant acceleration when the bod is moving along the positive -direction o (C) ange of a projectile ( ais) as a function of (r) its velocit ( ais) when projected at a fied angle o The square of the time period ( ais) of a (s) simple pendulum as a function of its length ( ais) o Sol. Ans p, s q, r, s (C) s q. Column I contains a list of processes involving epansion of an ideal gas. Match this with Column II describing the thermodnamic change during this process. Indicate our answer b darkening the appropriate bubbles of the matri given in the OS. Amit Institute for Competitive Eaminations : Phones: 61/, 557111///, 951-189/ - 1 -
Column I An insulated container has two chambers separated b a valve. Chamber I contains an ideal gas and the Chamber II has vacuum. The valve is opened. Column II IIT-JEE-8 (p) The temperature of the gas decreases. I ideal gas II vacuum An ideal monoatomic gas epands to twice (q) The temperature of the gas increases or its original volume such that its pressure remains constant 1 P V, where V is the volume of the gas (C) An ideal monoatomic gas epands to twice its original volume such that its pressure where V is its volume 1 P V /, An ideal monoatomic gas epands such that its pressure P and volume V follows the behaviour shown in the graph (r) The gas loses heat (s) The gas gains heat P V 1 V 1 V Sol. q p, r (C) p, r s, q. An optical component and an object S placed along its optic ais are given in Column I. The distance between the object and the component can be varied. The properties of images are given in Column II. Match all the properties of images from Column II with the appropriate components given in Column I. Indicate our answer b darkening the appropriate bubbles of the matri given in the OS. Column I Column II S (p) eal image Amit Institute for Competitive Eaminations : Phones: 61/, 557111///, 951-189/ - 11 -
IIT-JEE-8 S (q) Virtual image (C) S (r) Magnified image S (s) Image at infinit Sol. Ans p, q, r, s q (C) p, q, r, s p, q, r, s Amit Institute for Competitive Eaminations : Phones: 61/, 557111///, 951-189/ - 1 -