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fe two. fragments is, , la builer Yee 50 g with ‘a velocity, th this, the, gun is pushed back with, 1 The mass ofltne! gun is ||, (358), a0, 5 ke Wl, , , , (6) 22ms*, (pe O18! mrsiit|iii!l) tans 95], , sses 2.0 in bad 1.0 kg. The smaller mass, ed Of 80 ms". The total energy imparted to, , (b) 2.14 kj, | @ 4.8 ky [ATIMS 04], a) spring extends by x on loading, then the, , 7 energy ‘stored! by the spring is (if T is tension in the, spring and k is spring constant), , (@T? 2x (0) T? /2k, , esa? (@ 27? /k |!) Ans 974, | 14.4 spring 40 mm long is stretched by the, || application of a force. If 10 N force is required to, , stretch the spring through 1mm, then work done in, stretching the spring through 40 mm is, , , , , , , , , , , , , , , (0) 68 J, (d@) 8) [AIMS 98], , ||| 18. Consider the situation shown in the figure. A, hn spring) of spring constant 400 N/m is attached at one, end to a wedge fixed rigidly with the horizontal part., , , , , 7, Fl of, with a constant, , , , , , , fi the curved track. The minimum, in ni spring is nearly (take g = =10m/s?), , , , ©) 9.8m, | @ 009 km [AUMS 15], , , , + tats AN

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“together after collision, then, of system is, , , , , Hides wil ahs, , ck having mass ?t CO) les with ang, 2 A ra having mass 2m The lighter oe, | | | | after collision. Tf the velocity of «, | | l value of coefficient of Fest, , , , I, i, , |, (b) 04 |, (d) 0.8 (At,, A ball is bouncing down a flight of staite, Gent of restitution is e. The height Of each step gy), | Und the ball descends one step in each bounce, Aig}, OT | each bounce it rebounds to a height h above the i, 4 “lower step, The height is large enough compared wig, |, , i the impacts are effectiya, |, f the width of step so that th vey |, , in al Pa Find the relationship between hand d,, , , , , Hii el |, (hoa OO rai, , SAAN, , d d i, h=—— (dh =,)- iH, , Miia | all ala, , 95, If the linear momentum, is increased by 50%,, then kinetic energy will increase by i |, , | (@) 50% (2) 100% 1111) HHI, (c) 125% (d) 25% [ATIMS 16),, 26. A body moves from rest with a constant, acceleration. Which one of the following grap, represents the variation of its kinetic energy K withthe |, distance travelled x'?, , |, 1) © x |, , , , , , , , , , | [AIMS 95], H ial i . A a ig with speed of, , , , , , , , , , , , x, x, , @), , , , K*, , , , , , ’ fi \, , | [AIIM ‘61, net ih impinges directly on a similar ball at He, | all is brought to rest by the impact. If hal

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HA 6.97 4, L. Assertion, Mass arid energy are not conserved, , atately, but are conserved as a single entity called, mass-energy., , | Reason. Mass and energy are inter-convertible in, , | Accordance with Einstein’s relation, B= mic? |, 32. Assertion. In an elastic collision of two billiard, , alls) the totall kinetic energy is conserved during the, , ies ally with, | shore lime of collision of the balls (1.6, when they are in, , Waa mass i, at rest. Tf the Velocity of m, Contact)., , “after collision becomes 2 /3 times its initial velocity, the ||| | Reason. Energy spent against friction does not, , ratio of their masses is follow the law of conservation of energy. — [AIIMS 02], , , , , (1:5 Hin (2) 5:1 HA 33. Assertion. If momentum of a body increases by, (os UH A (d)2 BHI) 4) [Ans 16] 90%, its kinetic energy will increase by 125%., " 29. With what minimum speed 2 must a small ball Reason, Kinetic energy is proportional to square of, should be pushed inside a smooth vertical tube froma Velocity. [AIMS 2010], i height i, so that it may reach the top of the tube ? 34. Assertion. When a ball collides elastically with a, , | | floor, it rebounds with the same velocity as with it strikes., |) | Reason, Momentum of earth’ + ball system remains, constant, [AIMS 11], , (35. Assertion. In an elastic collision between two, bodies, the energy of each body is conserved., , , , , , , Reason. The total energy of an isolated system is, , conserved. [AIMS 13], of cross, 36. Assertion, In an elastic collision between two, bodies, the relative speed of the bodies after collision is, | equal to the relative speed before the collision., , i Reason. In an. elastic collision, the linear, JIMS 18] momentum of the system is conserved. [AIMS 15}, , @ Bg(h+2R), | ni, t OyeGR2h) 2g, / ‘|, , TL., fi Assertions and Reasons, , , , , , 37. Assertion. A quick collision between two, bodies is more violent than a slow collision, even when, Directions : In the following questions (30 - 40), a_ the initial and the final velocities are identical., statement of assertion is followed by a statement of |, reason. Mark the correct choice as, , (2) zt both assertion and reason are true and reason, is the correct explanation of the assertion., , |) Reason. The rate of change of momentum is greater, in the first case. [AIMS 14], , 8. Assertion, KE is conserved at every instant of, lastic collision., , , , , , , , (b) Ifboth assertion and reason are true but reason, is, , | Not correct explanation of the assertion, if, , | (2) If assertion is true, but reason is false, || 39, Assertion, A particle strikes head-on with, , | ® If both assertion and reason are false/assertion ANGER atationary Hantete such a eS at re, , 1S false and reason ignie Somes fo rest after collision. The collision should, f ‘ necessarily be elastic., , [AIMS 16], , , , , , , , , Reason. In. elastic collision, there is a loss of, ‘Momentum of the system of the particles. [AIMS 17], , | 40. Assertion. Work done in moving a body over a, closed loop is|zero for'every force in nature., , eason. Work done does not depend on nature of

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4 I | | J ;, Hy ticle lee mass 2 kg. Hence the particle is displaced, yar i, , from position (27+ ) metre to position (af 43 puby, , metre. The work done by the force on the particle ig, , @9I () 6), (13) (a) 15) INBET 14], 5 FP =(60i +15) -3k )N, cL and DHEA] 45K )m/s,, then instantaneous power is, tal (a) 195 watt (b) 45 watt, (0) 75 watt (@) 100 watt [CBSE PMT 2k], Se 6. A position dependent force, F = 7-243?) N, on, actson a small body of mass 2 kg and displaces it from, de x=0to x=5m. The work done in joule is.), (a) 135 (v) 270, id (c) 35 (@) 70 [CBSE PMT 97), 7.A force acts on a 3 g particle in such a way that, d the position of the particle as a function of time is given, , , , , , , , by x=3t—4#°+ 1°, where x is in metres and, seconds. The work done during the first 4 seconds., , (2) 490 mJ (b) 450 mJ 1, ‘ (c) 576 mJ @ 530 mJ BSE, 8.A body of mass 3 kg is under a constant, c metres in it, given by the relations |, ; HT, . seconds. Work done by the force in 2 seconds is, |, 19 5 AH, (a) = b) 2, (2) 5 J ( ) i9), 3 8, opr oy, , 9.A force F acting on an object varies wi, %as shown here. The force is in N and xin m, 1, , , , , , 4 7, d £(m) >, bce force in moving the object from x +0 to, 1807 13.5) HH, @45) | [CBSE PMT 05], , , , , , 10) Forte FGA a partiele moving ina straight,, Varies with distance das sHown in the figure. The work, done on the particle during its displacement of 12 mis., , , , , , (a) 18] (b) 21), (©) 26J (d) 13J [CBSE Pre 2011], , 11. A bomb of mass 30 kg at rest explodes into, two pieces of masses 18 kg and 12 kg. The velocity of, , 18 kg mass is 6ms”1. The kinetic energy of the other, mass is _, , (@) 324 J (b) 486 J, (©) 256) (4) 524 J, |12./A| mass of 1 kg is thrown up with a velocity of, , | 100 m/s. After 5 seconds, it explodes into two parts., , | One part of mass 400 g comes down with a velocity, | 25m/s,, , | The velocity of other part (take g=10ms *) is, , (a) 40 m/s F (b) 40 m/s +, , | (©) 100 m/s t (d) 60 m/s t, , | 13.4 ball of mass 2 kg and another of mass 4 kg are, , dropped together from a 60 feet tall building. After a, , fall of 30 feet each towards earth, their respective, Kinetic energies will be in the ratio of, , Li@v2s1 (be) 1:4, Hi ceyiaie2 (1:2 [cBSEPMroy, 14. A stationary particle explodes into two particles, , [CBSE PMT 051, , [CBSE PMT 2K], , sg!) Of masses m, and m, which move in Opposite directions, , with velocities 0, and v,. The ratio of their kinetic, energies E, / B, is, 1G) mm Ain, (b) m, /m,, (c) 1 (A) m2, / mv, [CBSE PMT 03], || 1S) A particle of mass m, is moving with a velocity, , | 9, and) another particle of mass m, is moving with a, , velocity %, Both of them have the same momentum, but their different kinetic energies are E, and E,, respectively, If my > My, then,, , | Em }, TE ag Ha, |) By Pa (a) BY SaaATDN TU