PHYSICS-24-12- 11th (J-Batch) Code-A WA

PART-C SUBJECTIVE: [4 × 9 = 36] There is NO NEGATIVE marking. 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. [Sol: F < N for Translational equilibrium i.e. F < 0.8 (20) F < 16  about O F(8) < 20(6) 20  6 F < 8 F < 15 Fmax = 15 Newtons ] Q.2 A ball of mass 1 kg moving with speed of 10 m/s on a smooth horizontal plane collides obliquely with another ball of same mass at rest as shown in the figure. If coefficient of restitution for the collision is 0.5, What will be the speed of the striking ball after the collision. [Sol: V + V1 = 5 (½) 5(1) = V1 – V Solving V =  5 4 speed = = = 8.75 m/s ] Q.3 An annular wheel (M.I. = 32 kgm2) hinged at its centre is rotating with initial angular velocity 10 rad/s in anticlockwise direction. If the inner radius is 5 cm, the outer radius is 20 cm and the wheel is acted upon by the constant forces shown in the figure, then what will be the angular velocity of the wheel after 10 sec. (Assume that the lever arm of all forces about centre remains constant) [Sol:  19(0.2) – 12(0.05) = 3.8 – 0.6 at t = 2 v  3 / 2 x = 0 ] 3  PART-B MATCH THE COLUMN [3 × 8 = 24] There is NEGATIVE marking. 0.5 Marks will be deducted for each wrong match. 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)] Q.2 Atruck of mass M crashes into a tempo of mass m < M and the two masses stick together. For each pair of quantities below, state the relationship Column I Column II Select the correct alternatives. (one or more than one is/are correct) [5 × 5 = 25] There is NO NEGATIVE marking. Q.16 A disc of mass m and radius r is gently placed on another disc of mass 2m & radius r. The disc of mass 2m is rotating with angular velocity 0 initially. The disc is placed such that axis of both are coincident. The coefficient of friction is  for surfaces of contact. Assume that pressure on disc is uniformly distributed. Find the correct statement. 1 (A) Loss in kinetic energy of system K = 3 mr2 2 . 1 (B*) Loss in kinetic energy of system K = 6 mr202 . (C*) The common angular velocity is 2  . 3 0 4 (D) The common angular velocity is 3 0 Q.17 A spring block system is placed on a rough horizontal floor. The block is pulled towards right to give spring some elongation and released. (A*) The block may stop before the spring attains its mean position. (B) The block must stop with spring having some compression. (C*) The block may stop with spring having some compression. (D) It is not possible that the block stops at mean position. Q.18 A ball of mass 1 kg bounces against the smooth ground as shown in the figure. The approaching velocity is 25 m/s and the velocity after hitting the ground is 15 2 m/s. Select the correct alternative(s) (A) Magnitude of Impulse = 5 Ns (B*) Magnitude of Impulse = 35 Ns (C*) Cofficient of restitution, e = 0.75 (D) Cofficient of restitution, e = 0.25 Q.19 A thin bar of mass M and length L is free to rotate about a fixed horizontal axis through a point at its end. The bar is brought to a horizontal position and then released. The angular velocity when it reaches the lowest point is (A) directly proportional to its length and inversely proportional to its mass (B) independent of mass and inversely proportional to the square root of its length (C) dependent only upon the acceleration due to gravity and the length of the bar (D) directly proportional to its length and inversely proportional to the acceleration due to gravity [Sol: I = 1 1 Ml2 3  L  2 I2 = Mg 2      =  Distance of P from C is 4l Ans: (C) ] 3 Q.9 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: l = 3.2 m, d = 1.2 × 10–3 m, Mg = y l A l yAl yd2l l = 1.6 × 10–3 m, y = 2 × 1011 Pa  M = gl  M = 4gl  M = 3.14  2 1011 1.44 106 1.6 103 4  9.8 3.2 kg  M  12 Kg (C) ] Q.10 A mass of 10 kg connected at the end of a rod of negligible mass is rotating in a circle of radius 30 cm with an angular velocity of 10 rad/s. If this mass is brought to rest in 10 s by a brake, what is the magnitude of the torque applied? (A*) 0.9 Nm (B) 1.2 Nm (C) 2.3 Nm (D) 0.5 Nm [Sol: m = 10kg, l = 0.3 m, 0 = 10rad/s, t = 10s I = ml2 = 0.9 Kgm2  = 0  0 t = 1 rad/s2  = I = 0.9 Nm (A) Q.11 Two blocks of masses 20 kg and 50 kg are lying on a horizontal floor (coefficient of friction  = 0.5). Initially string is just taut and blocks are at rest. Now two forces 235 N and 150N is applied on two blocks as shown in figure. What is acceleration of 20 kg block (g = 10 m/s2) (A) 0.5 m/s2 (B) zero (C*) 2.5 m/s2 (D) cannot be determined Q.12 A uniform sphere of weight W and radius 5 cm is being held by a string as shown in the figure. The wall is smooth . The tension in the string will be (A) 12 W / 5 (B) 13 W / 5 (C*) 13 W / 12 (D) 12 W / 13 [Sol: Tcos = W  T = W cos   cos = 12 13 PART-A Select the correct alternative. (Only one is correct) [15 × 3 = 45] There is NEGATIVE marking and 1 mark will be deducted for each wrong answer. Q.1 The S–shaped uniform wire shown in figure has a mass M, and the radius of curvature of each half is R. The moment of inertia about an axis through A and perpendicular to the plane of the paper is: (A) 3 MR 2 4 (B) MR2 (C) 3 MR 2 2 (D*) 2MR2 [Sol: IA = 2[MR2 + MR2] = 4MR2 Ans: IA = 2MR2 (D) ] 2 Q.2 Two rods OA and OB of equal length and mass are lying in xy plane as shown in the figure. Let Ix, Iy and Iz be the moments of inertia of both the rods about x-, y- and z-axis, respectively, then (A) Ix = Iy > Iz (B*) Ix = Iy < Iz (C) Iy < Ix < Iz (D) Iz > Iy > Ix [Sol: Ix = Iy < Iz (B) ] 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 minimum 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 = 105 Newtons F(30) = N(15) F = 5000 (D) ] Q.4 A ring of mass M and radius R is at rest at the top of an incline as shown. The ring rolls down the plane without slipping. When the ring reaches bottom, its angular momentum about its center of mass is: (A*) MR [Sol: Mgh = MV2 V = (B) MR (C) MR (D) none