12.Combined Test-2 (Paper-2)

RRR_CT-2_XII PAPER - 2 PART - I : PHYSICS SECTION - I Multiple Correct Answer Type This section contains 8 questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONE OR MORE is/are correct. 1. A wire of density 9  103 kg/m3 is stretched between two clamps 1 m apart and is stretched to an extension of 4.9  10 -4 metre. Young's modulus of material is 9  1010 N/m2. Then (A) The lowest frequency of standing wave is 35 Hz (B) The frequency of 1st overtone is 70 Hz (C) The frequency of 1st overtone is 105 Hz (D) The stress in the wire is 4.41 × 107 N/m2 2. A car moves towards a hill with speed vc. It blows a horn of frequency f which is heard by an observer following the car with speed v0. The speed of sound in air is v. (A) the wavelength of sound reaching the hill is v f (B) the wavelength of sound reaching the hill is v  vc f (C) The wavelength of sound of horn directly reaching the observer is v  vc f (D) the beat frequency observed by the observer is 2vc v  vo f v 2  v 2 3. Graph shows a hypothetical speed distribution for a sample of N gas particle (for V > V ; dN = 0, dN 0 dV dV is rate of change of number of particles with change veloicty) a dN dV (A) The value of aV0 is 2N. (B) The ratio Vavg/V0 is equal to 2/3. (C) The ratio Vrms/V0 is equal to 1/ 2 . V0 speed V (D) Three fourth of the total particle has a speed between 0.5 V0 and V0. 4. A particle is moving in a straight line according to graph given below : (a is acceleration, v is velocity, x is position, t is time) : a x (A) (B) (C) (D) x t 5. A particle is projected from ground at some angle with the horizontal. (Assuming point of projection to be origin and the horizontal and vertical directions to be the x & y axis) the particle passes through the points (3, 4) m and (4, 3) m during its motion then the range of the particle would be: (g = 10m/s2) (A) 36m (B) 37 m 7 (C) 4m (D) 16m 6. The system is released from rest with both the springs in unstretched position. Mass of each block is 1 kg and force constant of each spring is 10 N/m. Assume pulleys and strings are massless and all contacts are smooth. (g = 10 m/s2) (A) Extension of horizontal spring in equilibrium is 2/5 m (B) Extension of vertical spring in equilibrium is 1/5 m (C) Maximum speed of the block A is (D) Maximum speed of the block A is m/s m/s 7. Slider block A moves to the right with constant velocity 6 m/s in the arrangement as shown in the figure. C and D are points on the string . If choose correct option : VB , VC and VD are the velocities of B, C and D respectively then, (A)  VD  4 VB  VD   (C)  VC   VD  2 VB (D)  8. A particle is projected from the centre of the bottom of a wide well. Its diameter is 40 m and depth is 10 m. If the particle is projected with 20 m/s then, Find its angle (s) with vertical so that it comes out of the well. 1 (A) tan–1 2 Ans. (AB) 2 (B) tan–1 3 (C) tan–1 2 (D) tan–1 3 SECTION – II (Paragraph Type) This section contains 6 mulitiple choice questions relating to three paragraphs with two questions on each pargraph. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. Paragraph for Question Nos. 9 to 10 A smooth ball 'A' moving with velocity 'V' collides with another smooth identical ball at rest. After collision both the balls move with same speed with angle between their velocities 60°. No external force acts on the system of balls. 9. The speed of each ball after the collision is (A) V 2 V (B) 3 (C) (C) (D) (D) 10. If the kinetic energy lost is fully converted to heat then heat produced is (A) 1 mV2 3 (B) 2 mV2 3 (C) 0 (D) 1 mV2 6 Paragraph for Question Nos. 11 to 12 A sinusoidal wave travels along a taut string of linear mass density 0.1 g/cm. The particles oscillate along y-direction and wave moves in the positive x-direction. The amplitude and frequency of oscillation are 2mm and 50 Hz respectively. The minimum distance between two particles oscillating in the same phase is 4m. 11. The tension in the string is (in newton) (A) 4000 (B) 400 (C) 25 (D) 250 12. The amount of energy transferred (in Joules) through any point of the string in 5 seconds is 2 (A) 10 2 (B) 50 2 (C) 5 (D) Cannot be calculated because area of cross-section of string is not given. Paragraph for Question Nos. 13 to 14 A massless rod of length 2𝑙 has equal point masses 'm' attached at its ends (see figure). The rod is rotating with constant angular speed  about an axis passing through its stationary mid–point 'C' and always making angle '' with it as shown in figure. Consider both point masses as a system. 13. Kinetic energy of system is : (A) 4m𝑙22 (B) m𝑙22sin2 (C) m𝑙22cos2 (D) 2m𝑙22sin cos 14. → is the angular momentum of system about point 'C'. If magnitude of rate of change of → dL → is , then dt is : (A) m2𝑙2sin2 (B) 2m2𝑙2cos2 (C) 2m2𝑙2sin cos (D) 2m2𝑙2sin2 Paragraph for Question Nos. 15 to 16  4 – 3h  Figure shows a container having ideal liquid of variable density. The density of liquid varies as  = 0  h   0  where h0 is height of liquid in container, 0 is constant and h is distance measured from bottom of container. A solid small ball whose density is 5  and mass m is released from bottom of tank. ( Neglect viscous 2 0 effects). 15. The motion of the ball : (A) periodic but not SHM (B) SHM (C) oscillatory but not SHM (D) oscillatory but not periodic 16. After what time block reaches its initial position ? (A) 2 (B) 2 (C)  (D)  Matrix - Match Type 17. Volume versus pressure curves for n moles of an ideal gas are given for four process as shown in figure. Match the entries of column – I with the enteries of coloumn – II Column – I Column – II (P) For process 1 (1) Workdone is zero (Q) For process 2 (2) Workdone is maximum (R) For process 3 (3) Temperature will increase (S) For process 4 (4) Temperature will decrease P Q R S (A) 4 3 4 1 (B) 2 3 4 1 (C) 2 3 4 3 (D) 4 3 4 3 18. Figure shows four situations in which a small block of mass 'm' is released from rest (with respect to smooth fixed wedge) as shown in figure. Column-II shows work done by normal reaction on the block (with respect to an observer who is stationary on ground) till block reaches at the bottom of inclined wedge, match the appropriate column. Column–I Column–II h (A) 45° (p) Positive v = 2gh (B) h (q) Negative 45° h (C) (r) equal to mgh in magnitude (D) v = 2gh P h Q 45° R S (s) equal to zero (A) 1 2 4 2 (B) 2 1 3 4 (C) 1 1 4 2 (D) 4 3 1 2 19. A closed organ pipe P1 vibrating in its first overtone and another open organ pipe P2 vibrating in its third overtone, both pipes are in resonance with the tuning fork of frequency 12Hz. In column-II, the beat frequency in Hz is given when produced in conditions provided in column-I. Match the column-I and II Column-I Column-II (P) P1 resonate in 5th harmonic and P2 (1)  3 resonate in 3rd overtone (Q) P1 resonate in 1st overtone and P2 (2)  5 resonate in 3rd harmonic (R) P1 resonate in 9th harmonic and P2 (3)  8 resonate in 7th overtone (S) P1 resonate in 2nd overtone and P2 (4)  12 resonate in 4th overtone P Q R S (A) 4 1 3 2 (B) 2 1 3 4 (C) 2 1 3 4 (D) 3 1 4 2 20. A source of sound, emitting frequency of 6000 Hz, moving towards a stationary reflecting wall with speed 50 m/sec. There are four observes A,B,C and D as shown in figure. Speed of sound is 350 m/sec. Column–I contains observer and column–II contains the beat frequency observed by the observers. Match column–I with column–II. Column–I Column–II (P) observer A (1) 400 Hz (Q) observer B (2) 0(zero) Hz (R) observer C (3) 1750 Hz (S) observer D (4) 2000 Hz P Q R S (A) 2 1 3 4 (B) 1 2 3 4 (C) 3 2 1 4 (D) 3 1 2 4 ANSWERKEY 1. (AB) 2. (BCD) 3. (ABC D) 4. (A BCD) , 5. (B ) 6. (A B) 7. (A C D) 8. (AB) 9. (C) 10. (D) 11. (B) 12. (C) 13. (B) 14. (C) 15. (B) 16. (A) 17. (B) 18. (C) 19. (D) 20. (A)