2.COMBINED TEST-1 -PAPER-2

COMBINED TEST 1 PAPER-2 INSTRUCTIONS SECTION – I (Single Correct Answer Type) This section contains 8 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. A ring of mass m and radius R rolls on a horizontal rough surface without slipping due to an applied force ‘F’. The friction force acting on ring is : – F (A) 3 2F (B) 3 (C) F (D) Zero 4 2. A small area is removed from a uniform spherical shell of mass M and radius R. Then the gravitational field intensity near the hollow portion is - (A) GM R2 3GM (B) GM 2R2 (C) 2R2 (D) Zero R 3. A uniform metallic spherical shell of inner radius R has a thickness t, such that t = 1000. The shell is kept in vacuum and also, there is vacuum inside the shell. If absolute temperature of metallic spherical shell is R doubled, then the ratio of new radius to new thickness t will be (A) 2000 (B) 500 (C) 1000 (D) 2000 4. A sphere of mass m and radius r is projected in a gravity free space with speed v. If coefficient of viscosity of the 1 medium in which it moves is 6 , the distance travelled by the body before it stops is : mv (A) 2r mv (B) 2mv r mv (C) r (D) 4 r 5. A disc is performing pure rolling on a smooth stationary surface with constant angular velocity as shown in figure. At any instant, for the lower most point of the disc (A) Velocity is v, acceleration is zero (B) Velocity is zero, acceleration is zero (C) velocity is v, acceleration is v . (D) velocity is zero, acceleration is v R R 6. A narrow tube completely filled with a liquid is lying on a series of cylinders as shown in figure. Assuming no sliding between any surfaces, the value of acceleration of the cylinders for which liquid will not come out of the tube from anywhere is given by (A) gH 2L (B) gH L (C) 2gH L gH (D) 2L 7. When a ball is released from rest in a very long column of viscous liquid, its downward acceleration is ‘a’(just after release). Find its acceleration when it has acquired two third of the maximum velocity : a (A) 3 2a (B) 3 a (C) 6 (D) none of these 8. A small bead of mass m = 1 kg is carried by a circular loop having centre at C and radius r = 1 m which rotates about a fixed vertical axis. The coef f icient of f r iction between bead and loop i s µ = 0. 5. The maximum angular speed of the loop for which the bead does not have relative motion with respect to loop. (A) 5 (C) 15 2 1/ 2 2 1/ 2 (B) 10 (D) 30 2 1/ 2 2 1/ 2 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 Equation of displacement during SHM of a particle can be written as x = A cos t, x = A cos( t +  ) and 1 1 1 2 2 2 1 y = A cos( t +  ) here x and x are the displacement of a particle along x-axis during two different SHMs. y 3 3 2 1 2 is the displacement of the particle during SHM along y-axis. x and y axis are orthogonal to each other. Consider the super position of two SHMs along x-axis. Then the resultant displacement is x = x1 + x2 and resultant amplitude is A = [A 2 + A 2 + 2A A cos( –  )t]1/2 if    and  = 0. 1 2 1 2 1 2 1 2 1 Super position of two SHMs in perpendicular direction may result in SHM along a straight line or motion along a circle or an ellipse in clockwise or counter clockwise direction. 9. In superposition of two SHMs along x-axis identify the correct options : (A) If A1 = A2 and  =  the particle is always at rest (B) If  = 0, A1 = A2 and  is nearly equal to  then the resultant motion represent beat phenomenon with angular frequency  = 1  2 . 2 3 (C) If A = A ,    and  = 0 then the particle is at origin at time ‘t’ = 1  2 1 2 1 2 1 (D) If A = A ,  =  and  = 0 then the amplitude of resultant SHM is 2A 1 2 1 2 1 1 10. In superposition of two SHMs along perpendicular direction. Identify the correct options : A3 (A) If  =  and  = 0 then the resulting motion is SHM with amplitude 3 along line y = A1 x (B) If  =  , A = A and  = then the resulting motion is a circular motion in counter clockwise direction. 1 3 1 (C) If  =  , A 3 3  A and  2  = 2 then the resulting motion is elliptical in clockwise direction (D) If  =  and  =  then the resulting motion is elliptical in counter clockwise direction Paragraph for Question Nos. 11 to 12 Two closed identical conducting containers are found in the laboratory of an old scientist. For the verification of the gas some experiments are performed on the two boxes and the results are noted. Experiment 1. When the two containers are weighed WA = 225 g , WB = 160 g and mass of evacuated container WC = 100 g. Experiment 2. When the two containers are given same amount of heat same temperature rise is recorded. The pressure change found are PA = 2.5 atm. PB = 1.5 atm. Required data for unknown gas : 11. Identify the type of gas filled in container A and B respectively. (A) Mono, Mono (B) Dia, Dia (C) Mono, Dia (D) Dia, Mono. 12. Identify the gas filled in the container A and B. (A) N2, Ne (B) He, H2 (C) O2 , Ar (D) Ar, O2 Paragraph for Question Nos. 13 to 14 A sinusoidal wave is propagating in negative x–direction in a string stretched along x-axis. A particle of string at x = 2m is found at its mean position and it is moving in positive y direction at t = 1 sec. The amplitude of the wave, the wavelength and the angular frequency of the wave are 0.1meter, /4 meter and 4 rad/sec respectively. 13. The equation of the wave is (A) y = 0.1 sin (4t –1)+ 8(x – 2)) (B) y = 0.1 sin (t–1)– (x – 2)) (C) y = 0.1 sin (4t –1)–8(x – 2)) (D) none of these 14. The speed of particle at x = 2 m and t = 1sec is (A) 0.2 m/s (B) 0.6 m/s (C) 0.4 m/s (D) 0 SECTION — III (Multiple Correct Answer(s) Type) This section contains 6 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE may be correct. 15. Which of the following graph(s) represent retardation ? [v : velocity, t : time ; x : position] (A) (B) (C) (D) 16. Velocity time graph of two particle A and B starting from same point and travelling in same straight line is shown in figure. Then B may overtake A at time instant(s) : (A) t1 (B) t2 (C) t3 (D) t4 17. A particle is taken from A to B on given path. A force → is applied on this particle then, which of the following is/are correct : (A) If → is constant then work done by → on particle is → F. AB (B) If → is variable then work done by → on particle in → F. AB (C) Total work done on particle from A to B = kinetic energy at B – kinetic energy at A (D) Total work done on particle from A to B = mechanical energy at B – mechanical energy at A 18. A sound wave of frequency  travels horizontally to the right. It is reflected from a large vertical plane surface moving to left with a speed u. The speed of sound in medium is c. (c  u) (A) The number of waves striking the surface per second is c  c(c  u) (B) The wavelength of reflected wave is (c  u) (C) The frequency of the reflected wave as observed by the stationary observer is  (c  u) (c  u) u (D) The number of beats heard by a stationary listener to the left of the reflecting surface is c  u 19. A uniform disc of mass m and radius R rotates about a fixed vertical smooth axis passing through its centre with angular velocity  . A particle of same mass m and having velocity 2  R towards centre of the disc collides with the disc moving horizontally and sticks to its rim. (A) The angular velocity of the disc will become /3. (B) The angular velocity of the disc will become 5/3. (C) The impulse on the particle due to disc is 37 mR 3 (D) The impulse on the disc due to hinge is 37 mR 3 20. When the temperature of a copper coin is raised by 80 oC, its diameter increases by 0.2%, (A) percentage rise in the area of a face is 0.4% (B) percentage rise in the thickness is 0.4% (C) percentage rise in the volume is 0.6% (D) coefficient of linear expansion of copper is 0.25x10-4 /oC. ANSWER KEY TO COMBINED TEST - 01 (PAPER - 2) 1. (D) 2. (B) 3. (C) 4. (C) 5. (D) 6. (A) 7. (C) 8. (D) 9. (B) 10. (C) 11. (C) 12. (D) 13. (A) 14. (C) 15. (A,B,D) 16. (C,D) 17. (A,C) 18. (A,B,C) 19. (A,C,D) 20. (A,C,D) PART-2