9.RRR-1-XI-COMBINED TEST-1 (Paper-1)

RRR_CT-1_XI COMBINED TEST 1 PART - I : PHYSICS SECTION - I (Single Correct Answer Type) This section contains 10 multiple choice questions, Each question has four choices, (A), (B), (C) and (D) out of which ONLY ONE is correct. 1. A wall is moving with constant velocity u towards a fixed source of sound of frequency 'f'. The velocity of sound is 'v'. The wavelength of the sound reflected by the wall is - (A) v f v  u (B) f (C) (C) v  u (D) (D) v  u . v f v  u f 2. In the figure shown, a small block of mass m moves in fixed semicircular smooth track of radius R in vertical plane. It is released from the top. The maximum centrifugal force on the block at the lowest point of track is. (A) 3 mg (B) 2 mg (C) mg (D) zero 3. A uniform thin rod of mass m and length R is placed normally on surface of earth as shown. The mass of earth is M and its radius is R. Then the magnitude of gravitational force exerted by earth on the rod is (A) GMm 2R2 (B) GMm 4R2 (C) 4GMm 9 R2 (D) GMm 8R2 4. At the middle of the mercury barometer tube there is a little column of air with the length 𝑙0 and there is vacuum at the top as shown. Under the normal atmospheric pressure and the temperature of 300 kelvin, 𝑙0 = 10 cm. Neglect expansion of the tube. The length of the air column if the temperature rises to 330 kelvin will be - (A) 100 cm 11 (B) 11 cm (C) 10 cm (D) 12 cm 5. A transverse periodic wave on a string with a linear mass density of 0.200 kg/m is described by the following equation y = 0.05 sin(420t – 21.0 x) where x and y are in metres and t is in seconds. The tension in the string is equal to : (A) 32 N (B) 42 N (C) 66 N (D) 80 N 6. A uniform thin rod of mass ‘m’ and length L is held horizontally by two vertical strings attached to the two ends. One of the string is cut. Find the angular acceleration soon after it is cut : (A) g (B) g 2L L (C) 3g 2L (D) 2g L 7. Calculate moment of inertia of the system about axis AB shown in figure. Each segment of the system is made of a uniform wire of m mass per unit length  = r , where r is radius of each segment. The axis of full ring is along Y–axis. The axis of the semicircular rings are along x and z–axis. The centres of all rings coincide at the origin. mr 2 5 3 (A) 2 (B) 2 mr2 (C) 2 mr2 (D) 4 mr2 8. An aircraft moving with a speed of 972 km/h is at a height of 6000 m, just overhead of an anti-aircraft gun. If the muzzle velocity of the gun is 540 m/ s, the firing angle  for the bullet to hit the aircraft should be (A) 730 (B) 300 (C) 600 (D) 450 9. A train is running at a speed of 108 km/hr. An inspection cart is also moving with a speed 10m/s in the same e  1  direction as train. The train hits the cart    . The velocity of the cart after the collision is (in m/s) nearly.  (Assuming mass of train is much larger compared to mass of cart) (A) 20 (B) 40 (C) 50 (D) cannot determine as the masses of train and cart are not given. 10. An ice block at 0°C is dropped from height ‘h’ above the ground. What should be the value of ‘h’ so that it just melts completely by the time it reaches the bottom assuming the loss of whole gravitational potential energy is used as heat by the ice ? [Given : Lf = 80 cal/gm] (A) 33.6 m (B) 33.6 km (C) 8 m (D) 8 km SECTION – II (Multiple Correct Answers Type) This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE may be correct. 11. An ideal gas undergoes an expansion from a state with temperature T and volume V to V through three different polytropic processes A, B and C as shown in the P-V diagram. If E  , E  and A B E  be the magnitude of changes in internal energy along the three paths respectively, then : (A) E  < E  < E  if temperature in every process decreases A B C (B) E  > E  > E  if temperature in every process decreases A B C (C) E  > E  > E  if temperature in every process increases A B C (D) E  < E  < E  if temperature in every process increases B A C 12. A block of mass 2 kg is hanging over a smooth and light pulley through a light string. The other end of the string is pulled by a constant force F = 40 N. The kinetic energy of the block increase to 40 J in a given time interval (g = 10 m/s2). Then (A) tension in the string is 40 N (B) displacement of the block in the given interval of time is 2 m (C) work done by gravity is – 20 J (D) work done by tension is 80 J 13. A small object moves counter clockwise along the circular path whose centre is at origin as shown in figure. As it moves along the path, its acceleration vector continuously points towards point S. Then the object (A) Speed up as it moves from A to C via B. x (B) Slows down as it moves from A to C via B. (C) Slows down as it moves from C to A via D. (D) Speed up as it moves from C to A via D. 14. An insect of mass m, starts moving on a rough inclined surface from point A. As the surface is very sticky, the coefficient of friction between the insect and the incline is  = 1. Assume that it can move in any direction ; up the incline or down the incline then (A) The maximum possible acceleration of the insect can be 14 m/sec2 (B) The maximum possible acceleration of the insect can be 2 m/sec2 (C) The insect can move with a constant velocity (D) The insect can not move with a constant velocity 15. Two blocks of masses 3 kg and 6 kg rest on a horizontal smooth surface. The 3 kg block is attached to a spring with a force constant k = 900 Nm-1 which is compressed 2 m from beyond the equilibrium position. The 6 kg mass is at rest at 1m from mean position. 3kg mass strikes the 6 kg mass and the two stick together. (A) velocity of the combined masses immediately after the collision is 10 ms-1 (B) velocity of the combined masses immediately after the collision is 5 ms-1 (C) Amplitude of the resulting oscillation is 2 m (D) Amplitude of the resulting oscillation is 5/2 m. SECTION - III (Integer Answer Type) This section contains 5 questions. Answer each of the questions in a single-digit integer, ranging from 0 to 9. 16. A particle is moving along a straight line. Its velocity varies as v = 6 – 2t where v is in m/s and t in seconds. Find the difference between distance covered and magnitude of displacement in first 4 seconds. 17. If the acceleration of the block B in the following system is a (in m/s2) then find out value of 2a/5 (g = 10 m/s2): 18. A particle is executing SHM on a straight line. A and B are two points at which its velocity is zero. It passes through a certain point P (AP