PHYSICS 1. If and Le. The correc order of % error in (a) (b) x = y > z x < z < y x > z < y. A hollow verical cylinder of radius r and heigh h has a smooh inernal surface. A small paricle is placed in conac wih he inner side of he upper rim, a poin A, and given a horizonal speed u. angenial o he rim. I leaves he lower rim a poin B. verically below A. If n is an ineger hen (a) (b) 1
3. The person in he drawing is sanding on cruches. Assume ha he force exered on each cruch by he ground is direced along he cruch. If he coefficien of saic fricion beween a cruch and he ground is 0.90, deermine he larges angle ha he cruch can have jus before i begins o slip on he floor. (a) (b) 4. The sysem of wo weighs wih masses and are conneced wih weighless spring asshown. The sysem is resing on he suppor S. The suppor S is quickly removed. Theacceleraions of each of he weighs righ afer he suppor S is removed are. (a) (b)
5. Two small balls of mass m and m, respecively, are conneced by a hin and rigid bar wih negligible mass, and are free o slide on he 45 smooh inclines, as shown. Find he angle of he bar o he horizonal plane in equilibrium. The angle being negaive means ha he heavy ball is above he ligh ball. (a) 45 (b) 15 6. A man M slides down a curved fricionless rack, saring from res. The curve obeys he equaion y =. The angenial acceleraion of man is (a) g (b) 3
7. Beads A and B, each of mass m, are conneced by a ligh inexensible cord. They are consrained (resriced) o move on a fricionless ring in a verical plane as shown. The beads are released from res a he posiions shown. The ension in he cord jus afer he release is (a) mg (b) mg mg mg 8. Force of 100N is applied on a block of mass 3kg as shown in he figure. The coefficien of fricion beween he wall and block is 0.6. The magniude of he force exered by he wall on he block is (a)15n downwards 0N downwards (b)5n upwards 30N upwards 100N 1N 30 Ans. (A) F cos30 = N. N = 6 3 10.39 F sin 30 = 6N < sin So. F r will ac upward And F r max = N = 0.6 10.39 = 6.3 N. So force exered by wall = (6.3) (10.4) = 15N down ward 4
9. A block is placed on a rough horizonal plane. A ime dependen horizonal force F = K acs on he block. Here K is a posiive consan. Acceleraion-ime graph of he block is a a (b) (a) a a Ans : (C) 10. Block A is placed on block B, whose mass is greaer han ha of A. There is fricion beween he blocks, while he ground is smooh. A horizonal force P, increasing linearly wih ime, begins o ac on A. The acceleraions a 1 and a of A and B respecively are ploed agains ime (). Choose he correc graph. 5
a 1 a 1 a 1 a (a) a (b) a 1 a a 1a a a 1 a 1 a a Ans : (B) Because for some ime boh will move ogeher and afer ha B will move wih consan acceleraion due o kineic fricion and acceleraion of A will increase. 11. A block of mass M is conneced o a massless pulley and massless spring of siffness k. The pulley is fricionless. The spring connecing he block and spring is massless. Iniially he spring is unsreched when he block is released. When he spring is maximum sreched, hen ension in he rope is (a) zero (b) Mg Mg Mg/ K M Ans : (C) 1. A smooh wedge of mass m and angle of inclinaion ress unaached beween wo springs of spring consan k and 4k, on a smooh horizonal plane, boh springs in he unexended posiion. The 6
ime period of small oscillaions of he wedge (assuming ha he springs are consrained o ge compressed along heir lengh) equals (a) ( ) (b) ( ) ( ) none of he above 13. A car is moving owards souh wih a speed of 0 m/s. A moorcyclis is moving owards eas wih a speed of 15 m/s. A a cerain insan, he moorcyclis is due souh of he car and is a a disance of 50 m from he car. Find he shores disance beween he moorcyclis and he car (a) 0 m (b) 5 m 30 m 35 m Ans : (C) Taking N as + Y-axis and E as +X axis Imagine yourself as an observer siing inside he car. You will regard he car as being a res (a C). Relaive o you, he speed of he moorcyclis is obained by imposing he reversed velociy of car on moorcyclis as shown in he figure. 7
= 0 m/s ( ) The moorcyclis appears o move along he line MP wih speed 6 m/s. The shores disance = perpendicular disance of MP from C=d 14. A sone is dropped from he op of a ower. When i crosses a poin 5 m below he op, anoher sone is le fall from a poin 5 m below he op. Boh sones reach he boom of he ower simulaneously. Find he heigh of he ower.(ake g = 9.8 ) (a) 5 m (b) 35 m 45 m 55 m Ans: (C) Le us ake downward direcion as he posiive direcion. A ha momen when he firs sone crosses A, is velociy Le = ime aken by each sone o reach he ground afer he second sone is dropped. 8
( ) ( ) sec. ( ) 15. In an indusrial process 10 kg of waer per hour is o be heaed from 0 C o 80 C. To do his seam a 150 C is passed from a boiler ino a copper coil immersed in waer. The seam condenses in he coil and is reurned o he boiler as waer a 90 C. how many kg of seam is required per hour. (Specific hea of seam = 1 calorie per gm C, Laen hea of vaporisaion = 540 cal/gm) (a)1 gm (b)1 kg 10 gm 10 kg Ans : (B) Le he mass of seam required per hour be m kg. Hea gained by waer in boiler per hour is = 10 kg 1 kilo cal kg 1 C 1 (80 0) C = 600 kilo cal Hea los by seam per hour is = hea needed o cool m kg of seam from 150 C o 100 C + hea needed o conver m kg of seam a 100 C ino waer a 100 C + hea needed o cool m kg of seam a 100 C o 90 C = m 1 (150 100) + m 540 + m 1 (100 90) = 50 m + 540 m + 10 m = 600 m kilo cal 9
Hea los = hea gained. Equaing (1) and () we have 600 m = 600 or m = 1 kg 16. A caloriemeer conains 0.kg of waer a 30 C. 0.1 kg of waer a 60 C is added o i, he mixure is well sirred and he resuling emperaure is found o be 35 C. The hermal capaciy of he caloriemeer is (a)6300 J/K (b)160 J/K 400 J/K 50 J/K Ans : (B) Le X be he hermal capaciy of calorimeer and specific hea of waer = 400 J/kg-K Hea los by 0.1 kg of waer = Hea gained by waer in calorimeer + Hea gained by calorimeer 0.1 400 (60 35) 0. 400 (35 30) X (35 30) 10500 = 400 + 5X X = 160 J/K 17. Three liquids wih masses are horoughly mixed. If heir specific heas are and heir emperaures respecively, hen he emperaure of he mixure is (a) (b) Ans : (B) Check he dimension of he given opions. 18. A spring of force consan k is cu ino wo pieces such ha one pieces is double he lengh of he oher. Then he long piece will have a force consan of (a) (b) Ans : (B) If l1 nl hen k 1 ( n 1) k n 3 k [As n = ] 19. A clock which keeps correc ime a, is subjeced o. If coefficien of linear expansion of he pendulum is. How much will i gain or loose in ime (a)10.3 sec/day (b)0.6 sec/day 5 sec/day 0 min/day 10
T Ans : (A) 1 1 1 10 6 5 (40 0) ; T 1 10 86400 sec / day T sec/day. = 10.3 0. A lead bulle a 7 C jus mels when sopped by an obsacle. Assuming ha 5% of hea is absorbed by he obsacle, hen he velociy of he bulle a he ime of sriking (M.P. of lead = 37 C, specific hea of lead = 0.03 cal/gm C, laen hea of fusion of lead = 6 cal/gm and J = 4. J/cal) (a)410 m/sec (b)130 m/sec 307.5 m/sec None of hese 1 Ans : (A) Using expression obained in problem (11) we ge 75% mv J [ ms(37 7 ml ] 3 o 3 Subsiuing s 0.3 10 cal/ kg C and L 6 10 cal/ kg we ge v 410 m / s 1. An elecric fan is swiched on in a closed room. The air in he room is Ans : (B) (a)cooled (b)heaed Mainains is emperaure Heaed or cooled depending on he amospheric pressure. Three idenical rods made of he same maerial have been joined as shown in he figure. The free ends of he rods are mainained a emperaures as shown in he figure. The emperaure a he juncion of he hree rods is (a) (b) Paragraph quesion 3 & 4 The do in figure represens he iniial sae of a gas. An adiabaic div ides he p-v diagram regions 1 and as shown. ino 3. For which of he following processes, he corresponding hea supplied o he sysem Q is posiive 11
(a) he gas moves up along he adiabaic, (b) i moves down along he adiabaic, i moves o anywhere in region 1, i moves o anywhere in region. Ans : (D) 4. As he gas moves down along he adiabaic, he emperaure (a) increases (b) decreases remains consan variaion depends on ype of gas Ans : (B) Paragraph quesion 5, 6 & 7 In he following P-V diagram, wo adiabaics cu wo isohermals a and. moles of an ideal diaomic gas is aken hrough he cyclic process ABCDA. 5. In which process hea is absorbed by he gas. (a) DA (b) BC AB CD 6. The volumes a differen poins A,B,C & D are saisfy he following relaion (a) (b) 7. If is hea absorbed and is hea rejeced in one cycle hen- (a) (b) 1
8. A small block is sho ino each of he four racks as shown below. Each of he racks rises o he same heigh. The speed wih which he block eners he rack is he same in all cases. A he highes poin of he rack, he normal reacion is maximum in (a) (b) v v v v mv Ans : (A) Normal reacion a he highes poin of he pah R mg r For maximum R, value of he radius of curvaure (r ) should be minimum and i is minimum in firs condiion. 9. A wheel is subjeced o uniform angular acceleraion abou is axis. Iniially is angular velociy is zero. In he firs sec, i roaes hrough an angle In he nex sec, i roaes hrough an addiional angle The raio of is (a)1 (b) 3 5 Ans : (C) 1 From equaion of moion 1 1 1 0 () = [As 1 0, sec, 1 ] For second condiion 1 1 0 (4) [As 1 0, 4 sec, 1 ] 8 1 From (i) and (ii) 1, 6 3 1 30. Two blocks A and B of masses m and M respecively are placed on each oher and heir combinaion ress on a fixed horizonal surface C. A ligh sring passing over he smooh ligh pulley is used o connec A and B as shown. The coefficien of sliding fricion beween all surfaces in conac is. If A is dragged wih a force F hen for boh A and B o move wih a uniform speed we have (a) (b) C A B Ans : (D) 13