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SnniLVIBKANT ACADEIITY PttYstcsPractice Problems IRP-ITarget llT ADUAN CE-2O1 3India) Prirate LimitedDATE: 10/04/2013 TIME: 90 MIN. IRP DPP NO-I

Mechanics-1Single Ghoice Questions :1. Aparticleismovingalongthelocus: y =k.fi'(f >0) withaconstantspeed'v'. Att=0, itisattheoriginand

about to enter the first quadrant of x-y axes. At some later time t > 0, V, = vu. At this moment if acceleration.is a =ari +arj, then find [ar- ar]

2. In above question, the value of lal at the moment V, = Vy will be(A) 4k'

@T

@# (c) -4k' p)-#(A) u1 (B) zerol2k'l (D) None

(D) None

3. A ladder of length L is slipping with its ends against a vertical wall and a horizontal floor. At a certainmoment, the speed of the end in contactwith the horizontalfloor is v and the ladder makes an angle o = 30owith the horizontal. Then, the speed of the ladder's center must be

2vJ3A) (B) ;

4.

5.

6.

In above question, if + = 0 , the angular acceleration of the ladder when a = 45o isdt- ,r2(c) J2 E (D) None

A particle is projected with velocity 20 m/s, so that it just clears two walls of equal height 1 0 m, which are ata distance 20 m from each other. The time of passing between the walls is(A) 2s (B) zJzs (c)'6s (D) NoneThe diagram shows the variation of 1/v (where v is veloci$ of the particle) with respect to time. At time t =3 s using the details given in the graph, the instantaneous acceleration will be equalto

450

3s t(s)

(A) -2 m/sz (B) +3 m/sz (c) +s m/sz (D) -6 m/sz

I6

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7.trajectory ofparticle

\ particle at agiven instant

Figure shows path followed by a particle and position of a particelat any instant. Four different students have represented thevelocity vectors and acceleration vectors at the given instant.Which vector diagram can not be true in any situation?(ln each figure velocig is trangentialto the trajectory).

(A)Sita (C) Ram (D) ShyamA car is moving on a circular track with speed 10 m/sec. A man on the car throws a ball with inital speed uperpendicular to velocity of car relative to himself, choose the correct option,(A) Man can catch the ball(B) Ballfalls inside the circle(C) Ballfalls outside the circle(D) Man catches the ball exactly after completing one quarter circle

A force F = mg is acting on the block of mass m kept on a fixed rough wedge.The block is moving upwardswith constant velocity.Net force on the block from the wedge will be :(A) m9/2(B) mg/3(c) mg(D)msffi

(A) 1.6

Acomposite inclined plane having three different inclined surfaces AB,BC and CD of heights 1m each andcoefficients friction l,|^al respectively.A particle given an intiat velocity at A atong AB{3 {8 {15transverses the inclined surf.ace with uniform speed, reaching D is 5s. The intial velocity given is (in m/s)

8.

9.

- 't0.

(B) 1.8 (c) 2.4 (D) 3r?;rant Aeademy (I) Pvt. Ltd. "A-14(A)" Road No.1, Indraprastha IndustriatArea, Kota (Raj.) ph. 0744-2423/i06 t4

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12.

Subjective:11. At a given time, the distance recorder of a car showed 24942 km. At exactly two hours later the drivernoticed that it showed a symmetric number again. What was the average speed of the car in thistwo-hour leg ?

The velocity time graph of a particle is a parabola as shown inthe figure. The maximum value of velocity is equal to V.Calculate the distance covered by the particle in time

A motor boat moving up streams meets a raft moving down sFeam. After travelling for a period of t,, = 39min the boat reaches a landing place where it stops for a period of q= t hr. The boat then travels downstream and meets the raft in t. = 45 min. Find the cunent velocity u by assuming the speed of the boairelative to the water V = 8 km/hr.A swimmer enters a 97.5 m wide river at t = 0, at a point'P'on one bank. Point Q is located direcfly aerossP on the other bank. The river flow velocity is uniform and equalto 4 m/s. He cross the river by swimmingperpendicularly to the flow (with respect to water), at a speed (with respect to water) which keeps reducingwith time due to his physical exhaustion, at the constant rate of 4.2 m/s2. At t = 0, his speed was 8 m/s, Inhow much time does he cross the river? Also find the distance of the point where he lands on the otherbank, from Q. Sketch roughly his Earth frame locus through the river.A student launches an elastic ball from the ground level diiectly toward a tall vertical wall. After the firstlaunch, the ball bounces off the wall and then hits the ground. The student notices that the launch point isequidistant from the landing point and from the wall. The student then moves the launching point 20 m inthe direction perpendicular to the wall and launches the ball again. After the ball bounces off the wall andlands, the student notices that the distance between the launch point and the landing point is the same asit was the first time. Finally, the student launches the ball away from the wall. How far apart are the launchpoint and the landing point this time ? In all three cases, the initial velocity of the ball is the same.A blockA of mass 10 kg rest on second block B of mass 8 kg. The coefficient of friction at various surfacesis shown in figure.A horizontal force of 100 N is applied on upper block at t = 0, determine the veloc1y ofblock A relative to block B after 0.1 s of application of force.The system in initially at rest.Express youranswer in cm/s. Take g = 10 m/s2.

A particle of mass m moves linearly under the action of a timevarying force. The force time diagram is a parabola as shown inthe figure. The maximum value of the force is equal to X. Calculatethe displacement of the particle in time T.

Tt13.

14.

15.

16.

o)eotL17.

t-Tl2-+l

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19.

ln the figure shown, the mass of the hanging block is m, while that of the block resting on the floor is 3 m.The floor is horizontal and frictionless and all pulleys ideal. The system is initially held stationary with theinclined thread making an angle 0 = 30o with the horizontal. The blocks are now released from rest andallowed to move. The hanging block falls through a height'h' before hitting the floor. lt is found that thevalue of 0 becomes 600, when the hanging block hits the floor. Find the speed with which the hanging blockhits the floor, using energy conservation and kinematics. Also find (dO/dt) just before the hit.

Athinwalled uniform rigid cylinder of mass M has both its ends open. lt is held stationary on a flat horizontalsurface. lts height is 4R and radius R. Three smooth identical balls of mass f kg and radius (2R/3) eachare put inside the cylinder, one by one, untilthe system attains equilibrium in the two dimensional figurJshown. The centers of mass of the three balls and the center of cylinder lie in same vertical plane.

(A) Draw the free body diagram of the balls 1 ,2 and 3 and the cylinder.(B) Find the horizontal normal reactions N,', N, and N, exerted by the balls on the cylinder wall.Find the acceleration of an object O which moves without initial velocity along a helical grove of pitch h andradius r after completing n turns.

- 20.

11"

16.

r9. Nw,, = 20N, Nw, = 30N, Nw, = 191i1

55 Km/m 12.

17.

13.

18.

u = 2 km/hr. 14. Drift = 60 m 15. 60 m=+s=# v de 36and * =71i h

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