Kinematics-04-OBJECTIVE UNSOLVED

OBJECTIVE PROBLEMES LEVEL I 1. A particle parallel to x-axis as shown in the figure such that at all instant the y axis component of its position vector is constant and is equal to ‘b’. The angu- lar velocity of the particle about the origin is (a) v b (b) v sin  b O x (c) v sin 2  b (d) vb. 2. A stone is released from an elevator going up with acceleration 5 m/s2. The acceleration of the stone after the release is: (a) 5 ms-2 (b) 4.8 ms-2 upward (c) 4.8 down ward (d) 9.8 ms-2 down ward. 3. A swimmer wishes to reach directly opposite bank of a river, flowing with velocity 8 m/s. The swimmer can swim 10 m/s in still water. The width of the river is 480 m. Time taken by him to do so: (a) 60 sec (b) 48 sec (c) 80 sec (d) none of these. 4. The co-ordinates of a moving particle at any time t are given by x = ct2 and y = bt2. The speed of the particle is given by: (a) (c) 2t(c  b) t (b) 2t (d) 2t . 5. Choose the wrong statement (a) Zero velocity of a particle does not necessarily mean that its acceleration is zero. (b) Zero acceleration of a particle does not necessarily mean that its velocity is zero. (c) If speed of a particle is constant, its acceleration must be zero. (d) none of these. 6. The velocity - time graph of a linear motion is shown in figure. The displacement from the origin after 8 sec. is (a) 5 m (b) 16 m (c) 8 m (d) 6 m. V(m/s) - 7. A ball ‘A’ is thrown up vertically with speed u. At the same instant another ball ‘B’ is released from rest from a height h. At time t, the velocity of A relative to B is (a) u- (b) u – 2gt (c) (d) u  gt 8. The greatest height to which a man can throw a stone is h. The greatest distance to which he can throw will be: (a) h/2 (b) h (c) 2 h (d) 4 h. 9. A body starts from rest moves along a straight line with constant acceleration. The variation of speed v with distance s is given by graph v v (a) O s v (b) O s v (c) O s (d) . O s 10. A projectile is projected at an angle (  45º) with an initial velocity u. The time t, at which its horizontal velocity will equal the vertical velocity. (a) (c) t  u (cos   sin ) g t  u (sin   cos ) g (b) (d) t  u (cos   sin ) g t  u (sin 2   cos 2 ) g 11. The displacement-time graph of a moving particle is a inclined straight line. Therefore (a) its acceleration is constant (b) its velocity is constant (c) its displacement is constant (d) both its velocity and acceleration are uniform. 12. A train moving with a constant speed along a straight track takes a bend in a curve with the same speed. Due to this (a) its velocity is changed in magnitude (b) its velocity is not changed (c) its speed only is changed (d) its velocity is changed. 13. A body A of mass 4 kg is dropped from a height of 100 m.. Another body B of mass 2 kg is dropped from a height of 50 m at the same time. (a) Both the bodies reach the ground simultaneously. (b) A taken nearly 0.7 th of time required by B (c) B takes nearly 0.7th of time required by A (d) A takes double the time required by B. 14. On a displacement-time graph two straight lines make 30º and 60º with the time-axis. The ratio of the velocities represented by them is (a) 1: (c) 1 (b) 1 : 3 (d) 3 : 1. 15. If the maximum horizontal range for a projectile is R, the greatest height attained by it is (a) 4R (b) R/2 (c) 2R (d) R/4. LEVEL II 1. Two balls are dropped from the top of a high tower with a time interval of t0 second, where t 0 is smaller than the time take by the first ball to reach the floor which is perfectly inelastic. The distance S between the two balls, plotted against the time lapse ‘t’ from the instant of dropping the second ball is best represented by S S (a) O (b) t O t S S (c) (c) O (d) . t O t 2. The acceleration-time graph of a particle moving along a straight line is as shown in figure. At what time the particle acquires its initial velocity? (a) 12 sec. (b) 5 sec. (c) 8 sec. (d) 16 sec. a(m/s2) 10 t(sec.) 3. What are the speeds of two objects if they move uniformly towards each other, they get 4m closer in each second and if they move uniformly in the same direction with the original speeds they get 4m closer in each 10 sec? (a) 2.8 m/s and 1.2 m/s (b) 5.2 m/s and 4.6 m/s (c) 3.2 m/s and 2.1 m/s (d) 2.2 m/s and 1.8 m/s. 4. A particle has an initial velocity of (3ˆi  4 j) m/s and a constant acceleration of (4ˆi  3ˆj) m/s2. Its speed after one second will be equal to (a) 0 (b) 10 m/sec (c) 5 m/sec (d) 25 m/sec. 5. A particle is moving in a circle of radius R in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at t = 0 is v0 the time taken to complete the first revolution is (a) (c) R v0 R (1 e2 ) v0 (b) (d) v0 R R (e2 ) . v0 6. If the angle moving on a. () between velocity vector and the acceleration vector is 90 <  < 180. The body is (a) Straight path with retardation (b) Straight path with acceleration (c) Curvilinear path with acceleration (d) Curvilinear path with retardation. 7. The relation between time t and distance x is dation is: t  x 2  x where  and  are constants. The retar- (a) (c) 2v3 2v 2 (b) (d) 2v 2 22 v 3 . 8. Two particles start moving along the same straight line at the same moment from the same point. The first moves with constant velocity u and the second with constant acceleration f. The greatest distance between the particles before they meet once again is u (a) f f u 2 (b) 2f u 2 (c) (c) 2u 2 (d) f . 9. A man can swim at a speed of 5 km/h w.r.t. water. He wants to cross a 1.5 km wide river flowing at 3 km/h. He keeps himself always at an angle of 60º with the flow direction while swimming. The time taken by him to cross the river will be (a) 0.25 hr. (b) 0.35 hr. (c) 0.45 hr. (d) 0.55 hr. 10. The displacement of a particle in a straight line motion is given by s  1  10t  5t 2 . The correct repre- sentation of the motion is s (a) s (b) t t s (c) s (d) . t t 11. The position of a particle along x-axis at time t is given by x  1  t  t 2 . The distance travelled by the particle in first 2 seconds is (a) 1 m (b) 2 m (c) 2.5 m (d) 3 m. 12. From the velocity-time graph of a particle moving in a straight line, one can conclude that (a) its average velocity during the 12 seconds interval is 24/7 m/s (b) its velocity for the first 3 seconds is uniform and is equal to 4 m/s (c) the body has a constant acceleration between t =3s V(m/s) 4 m/s A B and t = 8s O 3 (d) the body has a uniform velocity from t = 8s to t = 12 s. C 8 12 Time(in s) 13. The displacement x of a particle along the x-axis t time t is given by x  a  a1 t  a 2 t 2 . The accel- eration of the particle is 0 2 3 (a) a  a1 (b) a1  a 2 (c) 0 2 a  a1  a 2 (d) 2 3 2a 2 . 0 2 3 3 14. A particle moves with constant acceleration for 6 seconds after starting from rest. The distances travelled during the consecutive 2 seconds interval are in the ratio (a) 1 : 1 : 1 (b) 1 : 2 : 3 (c) 1 : 3 : 5 (d) 1 : 5 : 9. 15. The velocity-time graph of a body moving along a straight line is as follows: The displacement of the body in 5 s is (a) 5 m (b) 2 m (c) 4 m (d) 3 m. 2 m/s 1 -1 -2 16. A particle is projected vertically upward from A with a speed of 50 m/s and another is dropped simul- taneously from B, which is 200 m vertically above A. They cross each other after (a) 4 s (b) 5 s (c) 6 s (d) 8 s. 17. A cannon ball has the same range R on a horizontal plane for two angles of projection. If h1 and h 2 are the greatest height in the two paths for which this is possible, then (a) (c) R  h1h 2 R  3 (b) (d) R  4 R  (h1h 2 )1/ 4 . 18. A ball rolls off the top a staircase with a horizontal velocity u ms1 . If the steps are h m high and w m wide the ball will hit the edge of the nth step if (a) gw 2 n  2hu 2 2u 2 (b) 2hu 2 n  gw 2 2hw 2 u 2 (c) n  gw 2h (d) n  g