Title 1. W.P.E. (Pass.Q.) E.pdf ✅

PHYSICS Passage # 2 (Ques. 4 to 6) A particle is attached between two ideal identical springs and the other ends of springs are kept fixed at points A and B on the horizontal plane. Springs are also horizontal such that the whole arrangement lies on the horizontal plane as shown in figure. Initially at t = 0 the particle is at point O and in this position both springs are unstretched then the particle is pulled very slowly perpendicular to the initial straight line AOB upto point P on the horizontal plane and released at t = t0. B P O L L x A Q.4 Work done by the external agent from t = 0 to t = t0 to pull particle from point O to point P if spring constant of each spring is K is – (A) W = Kx2 (B) W = Kx2 + 2Kx [x – 2 2 L + x ] (C) W = Kx2 + 2KL [L + 2 2 L + x ] (D) W = Kx2 + 2KL [L – 2 2 L + x ] Sol. [D] W = k Wext + Ws = 0 Wext = – W s =       + − 2 2 2 k( L x L) 2 1 × 2 Q.5 If the horizontal surface is frictionless, mass of particle is 0.8 kg, spring constant K is 1000 N/m, L is 1.2 m and x is 0.5 m then speed of particle when it reaches point O is – (A) 4 m/s (B) 5 m/s (C) 2 m/s (D) None of these Sol. [B] W = k = 2 1 mv2        + − 2 2 2 k( L x L) 2 1 × 2 = 2 1 mv2 Q.6 If in the above horizontal surface is rough with friction coefficient μ between particle and surface and mass of particle is 0.8 kg, spring constant is 1000 N/m. The length L is 1.2 m and the distance x is 0.5 m, then the value of μ if particle just reaches point O is – (A) 0.4 (B) 0.8 (C) 2.5 (D) 5 Sol. [C] W = k Ws + Wf = 0 W f = – Ws – mgx = –       + − 2 2 2 k( L x L) 2 1 × 2 Passage # 3 (Ques. 7 to 9) A body of mass 10 kg moving along x-axis has velocity 4m/s at x = 0. The acceleration and potential energy of the body varies as shown in following figures. a(m/s2 ) 2 4 8 x(m) U(J) +120 4 8 x(m) –120 Sol.7[ B], 8[C], 9[A] Area of a - x curve gives = 2 1 (v2 – u 2 )  2 1 (v2 – u 2 ) = 12  K = 2 1 × 10 × (v2 – u 2 ) = 120 J as 2 1 (v2 – u 2 ) = 12  K = 2 1 mv2 = 200 J also Wext. = –U and  Wext. + Wc = K Q.7 Work done by conservative forces when body moves from x = 0 m to x = 8 m is- (A) 120 J (B) 240 J (C) –120 J (D) –240 J
Q.8 Work done by external forces when body moves from x = 0 m to x = 8m is- (A) 120 J (B) 240 J (C) –120 J (D) –240 J Q.9 The change is kinetic energy when body moves from x = 0 m to x = 8 m is- (A) 120 J (B) 240 J (C) –120 J (D) –240 J Passage # 8 (Qus. 10 to 12) The amount of energy a car expends against air resistance is approximately given by E = 0.2 air ADv2 where E is measure in Joules. air is the density of air (1/2 kg/m3). A is the cross-sectional area of the car viewed from the front (in m2), d is the distance traveled (in m), and v is the speed of the car (in m/s). Julie wants to drive from Tucson to Phoenix and get good gas mileage. For the following questions, assume that the energy loss is due solely to air resistance and there is no wind. Q.10 If Julie increases her speed from 30 mph to 60 mph, how does the energy required to travel from Tucson to Phoenix change? (A) It increases by a factor of 2 (B) It increases by a factor of 4 (C) It increases by a factor of 8 (D) It increases by a factor of 16 [B] Sol. If v increases by a factor of 2, then the required energy increases by a factor of 22 = 4. Q.11 Julie usually drives at a certain speed. How much more energy will she use if she drives 20% faster? (A) 20% more energy (B) 40% more energy (C) 44% more energy (D) 80% more energy [C] Sol. If Julie increases her speed by 20%, then she multiplies her speed by 1.2. Thus the required energy is multiplied by (1.2)2 = 1.44, which is an increase of 44%. Q.12 Scott drives a very large 50s style car, and Laura drives a small 90s style car, so that every linear dimension of Scott's car is double that of Laura's car. On the basis of energy loss due to air resistance alone, how much more energy would you expect Scott's car to expend getting from Tucson to Phoenix than Laura's car? (A) Twice as much as energy (B) Four times as much energy (C) Eight times as much energy (D) Sixteen times as much energy [B] Sol. Comparing Scott’s car to Laura’s, all the linear dimensions are increased by a factor of 2 (see figure). The cross–sectional area A is width times height (A = hw), so if both h and w increase by factor of 2, then A increases by a factor of 4. Thus the required energy increases by a factor of 4, the increase in length does not matter. A1 A2 h  w Passage 9: (Q. 13 to 15) The human circulatory system can be thought of as a closed system of interconnecting pipes through which fluid is continuously circulated by two pumps. The two pumps, the right and left ventricles of the heart, work as simple two- stroke force pumps. The muscles of the heart regulate the force by contracting and relaxing. The contraction (systole) lasts about 0.2 s, and a complete systole/diastole (contraction/relaxation) cycle lasts about 0.8 s. For blood pressures and speeds in the normal range, the volume flow rate of blood through a blood vessel is directly proportional to the pressure difference over a length of the vessel and to the fourth power of the radius of the vessel. The total mechanical energy per unit volume of blood just as it leaves the heart is: E/V = gh + P + 2 1 v 2