PHYSICS-24-12- 11th (J-Batch)

PART-C SUBJECTIVE: [4 × 9 = 36] Q.1 An isosceles prism of mass 2 kg rests on a rough horizontal surface with coefficient of friction  = 0.8. Sides of triangular cross-section of prism are 10 cm, 10 cm and 12 cm as shown. A horizontal force F is applied on the prism as shown in the figure . Find maximum magnitude of F (in newton) for which the prism stays inequilibrium. [Ans. 15 N] [Sol. In the case of rotation equilibrium just before toppling FBD h = 102  62 = 64 = 8 Taking moment about point O  F . 8 = w . 6 F = 6 w 8 = 3  2 10 = 15 N 4 In the case of translation equilibrium F = f = N = 0.8 × 2 × 10 = 16 N  Maximum F = 15 N for equilibrium F = 15 N ] Q.2 A solid cylindrical copper rod 0.200 m long has one end maintained at a temperature of T Kelvin. The other end is blackened and exposed to thermal radiation from surrounding walls maintained at 400 K. The sides of the rod are insulated, so no energy is lost or gained except at the ends of the rod. When steady state is reached, the temperature of the blackened end is 200 K. What is the value R  T = 2 R = 2  T ] PART-B MATCH THE COLUMN [3 × 8 = 24] INSTRUCTIONS: Column-I and column-II contains four entries each. Entries of column-I are to be matched with some entries of column-II. One or more than one entries of column-I mayhave the matching with the same entries of column-II and one entryof column-I mayhave one or more than one matching with entries of column-II. Q.1 Match the physical situation of Column I with the graph of Column II. The graphs depict the variation of total energy (solid), potential energy (long dashes) and kinetic energy (short dashes) with time. Column I Column II (A) A mass on a spring released from compression (P) until it reaches its maximum extension (B) An object in circular orbit around the sun (Q) (C) An object undergoing free fall (R) (D) An object being pulled on a level, frictionless (S) surface by a constant force in the horizontal direction [Ans. (A) Q, (B) S, (C) R, (D) P] [Sol. (A) E = constant, KE = 1 mv2 , E = U + K.E., U= E–K.E =  – t2 2 (B) v = 0, v = constant, U =  GMm , K.E. = 1 m v2 = constant,  E = constant r c R 2 c P = nV2– mV1 = 1 × 15 – 1 × (–20) = 35 kg m/s Impulse exerted by ground = P 35 Ns Ans. ] Select the correct alternatives. (one or more than one is/are correct) [5 × 5 = 25] There is NO NEGATIVE marking. Q.16 Four identical rods which have thermally insulated lateral surfaces are joined at point A. Points B,C,D & E are connected to large reservoirs. If heat flows into the junction from point B at rate of 1 W and from point C at 3 W inside, flows out from D at 5 W, which relation(s) is/are correct for temperature of these points ? (A*) TA < TE (B) TB = TC (C*) TC > TD (D*) TB = TE [Sol. Heat flow At A x + 1 + 3 = 5 x = 1 Heat in flows from E  T > T  T > T > T TB – TA = TE – TA  T = T ] Q.17 The kinetic energy of a particle depends on the reference frame of the observer. In an exoergic reaction, the total final kinetic energy is greater than the total initial kinetic energy. In an endoergic reaction, the total final kinetic energy is less than the total initial kinetic energy. Which of the following is correct? (A*) Areaction that is exoergic in one inertial reference frame is exoergic in all inertial reference frames (B) It is possible to find a reference frame in which an exoergic reaction could appear to be endoergic (C) It is possible to find a reference frame in which an endoergic reaction could appear to be exoergic (D*) A reaction that is endoergic in one inertial reference frame is endoergic in all inertial reference frames. [Sol. The difference of total K.E. for reaction in any frame is same.] Q.18 At 0°C a body emits: (A) no radiation (B) electromagnetic radiation of single wavelength [Sol.  of weight of rod AB >  of weight of rod BC about point of suspension] Q.9 Three identical vessels have gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic), and the third contains uranium hexafluoride (polyatomic). If n1, n2, n3 be the number of moles and v1, v2, v3 the rms velocity of gases in vessel 1, 2 and 3 respectively, then (A) n1 > n2 > n3 & v1 > v2 > v3 (B) n1 < n2 < n3 & v1 < v2 < v3 (C) n1 = n2 = n3 & v1 = v2 = v3 (D*) n1 = n2 = n3 & v1 > v2 > v3 [Sol. Avogadro law & v = ] Q.10 The chlorophyll in most plants is largely responsible for promoting photosynthesis and is also responsible for the green color we observe in most plants. Which of the following colors of light would be the least useful for photosynthesis in plants? (A) magenta (B) red (C*) green (D) blue Q.11 The room heater can provide only 16ºC in the room when the temperature outside is -20ºC. It is not warm and comfortable, that is why the electric stove with power of 1 kW is also plugged in. Together these two devices maintain the room temperature of 22ºC. Determine the thermal power of the heater. (A) 3 kW (B) 4 kW (C) 5 kW (D*) 6kW [Sol. Rate of heat loss with only room heater Q Pn = t = C (16 + 20) C = constant while both heater and stove it is  Q ' Pn + Ps =  t  = C (22 + 20) Pn  Pn + Ps 36 = 42  7P = 6 P + 6P  P = 6P = 6 kW ] Q.12 A recording disc rotates steadily at n1 rps on a table. When a small mass m is dropped gently on the disc at a distance x from its axis, it sticks to the disc, the rate of revolution falls to n2 rps. The original moment of inertia of the disc about a perpendicular axis through its centre is mx2 n mx2 n mx2 n mx2 (A) I = n1  n2 (B) I = 1 n1  n2 (C*) I = 2 n1  n2 (D) I = 2 n1 [Sol. Initially angular momentum = I (2n1) Final angular momentum = (I + mx2 )(2n2) L is conserved as ext = 0  I n1 = (I + mx2) n2 Q.3 Figure shows a pair of pin jointed gripper tongs holding an object weighing 2000 N. The coefficient of friction  at the gripping surface is 0.1. X-X’ is the line of action of the input force and Y-Y’ is the line of application of normal gripping force. If the pin-joint is assumed as frictionless, the magnitude of force F required to hold the weight is (A) 1000 N (B) 2000 N (C) 2500 N (D*) 5000 N [Sol. 2N = 2000  N = 10000 N also F × 30 = N × 15  F = 5000 N ] Q.4 A T shaped object with dimensions shown in the figure is lying on a smooth floor. Aforce F is applied at the point P parallel to AB such that the object has only the translational motion without rotation. Find the location of P with respect to C. (A) (3/4)l (B) l (C*) (4/3)l (D) (3/2)l [Sol. Only translation is possible if force is applied at center of mass cm = 2m.l + m.2l = 3m 4 3 l ] Q.5 A steel wire, 3.2 m long, has a diameter of 1.2 mm. The wire stretches by 1.6 mm when it bears a load. Young's modulus for steel is 2.0 × 1011 Pa. The mass of the load is closest to: (A) 24 kg (B) 28 kg (C*) 12 kg (D) 20 kg [Sol. We know that F l A = Y l A  mg A l l = Y l i.e. m = g Y l (0.6 103)2  2 1011 1.6 103 = 10  3.2