May 2011 - Career Point

shown in the figure. We use the sign conventionin which position or momentum upwards (or toright) is positive and downwards (or to left) isnegative.22m v − m u = 2mp 2 2– p 0 = 2m 2 gxp 2 = p 2 0 + 2m 2 gx222gxMomentumPosition35. The phase space diagram for a ball thrownvertically up from ground is-Momentum36. The phase space diagram for simple harmonicmotion is a circle centered at the origin. In thefigure, the two circles represent the sameoscillator but for different initial conditions, andE 1 and E 2 are the total mechanical energiesrespectively. Then-MomentumE2a2aE 1Position(A)PositionMomentumAns.Sol.(A) E 1 = 2 E 2 (B) E 1 = 2E 2(C) E 1 = 4E 2 (D) E 1 = 16 E 2[C]K' E Max 1(B)PositionK' E max 2K.E 1 = 0Momentummaximal positionmaximal positionK.E 2 = 0(C)PositionMomentumEE1k(2a)21 2k(a)221= =2E 1 = 4E 24(D)Position37. Consider the spring-mass system, with the masssubmerged in water, as shown in figure. Thephase space diagram for one cycle of this systemis-Ans.Sol.[D]From conservation of mechanical energy1 2 1 2mv + mgx = mu22XtraEdge for IIT-JEE 70 MAY 2011