Solution - Career Point

32. A large number of particles are moving with samemagnitude of velocity v but having randomdirections. The average relative velocity between anytwo particles average over all the pairs is50 N(A) 4π v (B) 2π v (C) π3 v (D) π4 v33. A body is moving with uniform speed v on anhorizontal circle from A as shown in the fig. Changein the velocity in the first quarter revolution isOv 1AWE2 kg5 kg(A) 0, 2.5 ms –2 (B) 0, 0(C) 2.5 m/s 2 , 2.5 m/s 2 (D) 1 m/s 2 , 2.5 m/s 237. In the shown system m 1 > m 2 . Thread QR is holdingthe system. If this thread is cut, then just after cutting(A) v 2 north (B) 2 v south west(C) 2 v north-west (D) 2v westS34. A hollow vertical drum of radius r and height H has asmall particle in contact with smooth inner surface ofthe upper rim at point P. The particle is given ahorizontal speed u tangential to the rim. It leaves thelower rim at Q vertically below P. Taking n as aninteger for number of revolution we getP u(A) n =(C) n =2πrHu2π r2H / gHQ(B)(D) n =2πr2H / gu2πr2H / g35. A balloon is descending at a constant acceleration a.The mass of the balloon is M. When a mass m isreleased from the balloon is starts rising withacceleration a. Assuming that volume does notchange when the mass is released, what is the valueof m.(A)(C)2a⎛ a + g ⎞M (B) ⎜ ⎟ M(a + g)⎝ 2a ⎠2a(a + g)M(D)Maa + g36. Two blocks of masses 2 kg and 5 kg are at rest onground. The masses are connected by a string passingover a frictionless pulley which in under theinfluence of a constant upward force F = 50 N. Theaccelerations of 5 kg and 2 kg masses arem 2QR(A) Acceleration of mass m 1 is zero and that of m 2 isdirected upward(B) Acceleration of mass m 2 is zero and that of m 2 isdirected downward(C) Acceleration of both the block will be same(D) Acceleration of system is given by⎛ m ⎞⎜1 − m2⎟ kg, when k is the spring factor⎝ m1+ m2⎠38. A car of mass M accelerates starting from rest.1/ 2⎛ 2pt ⎞Velocity of the car is given by v = ⎜ ⎟ , where p⎝ M ⎠is the constant power supplied by the engine. Theposition of car as a function of time is given as⎛ 8p⎞(A) ⎜ ⎟⎠⎝ 9M⎛ 8p⎞(C) ⎜ ⎟⎠⎝ 9M1/ 2t 3/21/ 2m 1⎛ 9p⎞(B) ⎜ ⎟⎠⎝ 8Mt 2/3 ⎛ 9p ⎞(D) ⎜ ⎟⎝ 8M ⎠1/ 2t 3/239. Six identical uniform rods PQ, QR, RS and ST, TV,UP each weighing w are freely joined at their ends toform a hexagon. The rod PQ is fixed in a horizontalposition and middle points of PQ and ST areconnected by a vertical string. The tension in string isP QUT S(A) W (B) 3W (C) 2W (D) 4WRt 3XtraEdge for IIT-JEE 79APRIL 2010