Title 1-single-correct-answer-type-.pdf ✅

Kinematics of a Particle Motion in Two Dimension 1. A car moves rectilinearly from station A to the next station B (rest to rest) with an acceleration varying according to the law f = (a − bx), where a and b are constants and x is the distance from the station A. The distance between the two stations and the maximum velocity are : (A) a b , √a b (B) b 2a , a b (C) 2a b , b √a (D) 2a b , a √b 2. The displacement-time graph of a moving particle with constant acceleration is shown in the figure. The velocity-time graph is given by (A) (B) (C) (D) 3. Acceleration (a) displacement (s) graph of a particle moving in a straight line is as shown in the figure. The initial velocity of the particle is zero. The v-s graph of the particle would be :
(A) (B) (C) (D) 4. Two balls are thrown from an inclined plane at angle of projection α with the plane, one up the plane while other down the inclined plane (as shown in figure). In the figure u1 and u2 are the speeds when the line of motion of the particle is parallel to the inclined plane and h1 and h2 are maximum displacements perpendicular to inclined plane respectively. (i) h1 = h2 = u 2 sin2 α 2 gcos θ (ii) T1 = T2 = 2usin α gcos θ = T (iii) R1 = R2 = gsin θ ⋅ T 2 (iv) u1 = u2 The correct choice is : (A) All are true (B) Statements (i) and (ii) are true (C) Statements (i), (ii) and (iii) are true (D) Statements (i), (ii) and (iv) are true
5. A particle is thrown with an initial velocity v0 at an angle α to the horizontal. The ratio of radius of curvature at the highest point of its path to the maximum height is : (A) 1 2 cot α (B) 2cot2 α (C) 2cot α (D) 1 2 cot2 α 6. The distance between two moving cars A and B at a particular time is d. Their relative velocity is V with the component along AB being u and perpendicular to AB being v. The time that elapses before they arrive at their nearest distance is : (A) du V2 (B) dv V2 (C) d(u+v) V2 (D) dV (u+v) 2 7. Two particles positioned at A(5, 3) and B(7, 3) are moving with constant velocity 2i 3j and xi yj respectively. After 2s they collide, then the values of x and y are respectively (A) 2,2 (B) 1,3 (C) 3,2 (D) 1,1 8. Three particles A, B and C are projected with initial velocities vA, vB and vC (in vertical plane) as shown in figure. The particles collide at highest point of A. Then vA: vB: vC is : (A) 1: 2:√3 (B) √3: 2: 1 (C) √3: 1: 2 (D) Data insufficient 9. The acceleration of a particle which moves along the positive x-axis varies with its position as shown. If the velocity of the particle is 0.8 m/s at x = 0, the velocity of the particle at x = 1.4 is : (in m/s ) (A) 1.6 (B) 1.2 (C) 1.4 (D) None of these 10. A ball is hit by a batsman at an angle of 37∘ as shown in figure. The man standing at P should run at what minimum velocity so that the catches the ball before it strikes the ground. Assume that height of man is negligible in comparison to maximum height of projectile. (A) 3 ms−1 (B) 5 ms−1 (C) 9 ms−1 (D) 12 ms−1 11. A ball is thrown from a point on ground at some angle of projection. At the same time a bird starts from a point directly above this point of projection at a height h horizontally with speed u. Given that in its flight ball just touches the bird at one point. Find the distance on ground where ball strikes (A) 2u√ h g (B) u√ 2h g (C) 2u√ 2h g (D) u√ h g 12. A ball is projected normally from point P (which is on an inclined plane) with speed 10 m/s strikes the wall normally. If all the collisions are perfectly elastic, then the time period of periodic motion is :
[Take g = 10 m/s 2 ] (A) √2sec (B) 2√2sec (C) 3√2sec (D) 4√2sec 13. A particle is projected with velocity u⃗ at an angle θ with the horizontal as shown in the figure. h, T and R are maximum height, time of flight and range respectively. (A) magnitude of average velocity between A and B is ucos θ (B) time required to go from A to B is T/3 (C) Magnitude of average acceleration between A and B is 2 g (D) Instantaneous velocity at A and B will be same 14. A particle is projected from point A at an angle of 53∘ with horizontal. At the same time wedge starts from rest and moves with constant acceleration a as shown. The value of a for which the particle strikes the plane perpendicular to it at point P is : (tan 53∘ = 4 3 ) (g = 10 m/s 2 ) (A) 10 m/s 2 (B) 100 m/s 2 (C) 26/3 m/s 2 (D) 140 m/s 2 15. The radii of the front and rear wheels of a carriage are a and b respectively and c is the distance between the axles. A dust particle driven from the highest point of the rear wheel is observed to settle on the highest point of the front wheel. The velocity of the particle with respect to the carriage is : (C) √g √(c + b − a)(c + a − b) √4(b + a) √g √(a + b + c)(a − b + c) √4(b − a) √g √(a + b + c)(a + b − c) √4(b − a) √g √(c + b − a)(c + a − b) √4(b − a) MULTIPLE CORRECT ANSWERS TYPE Each of the following Question has 4 choices A, B, C & D, out of which ONE or MORE Choices may be Correct: 16. A ball of mass m is projected from the ground with an initial velocity u making an angle θ with the horizontal. Then choose the correct statement(s). (A) the change in velocity between the point of projection and the highest point is usin θˆj (downward) (B) the average velocity averaged over the time of flight is ucos θiˆ (horizontal) (C) the change in velocity in the complete projectile motion is −2usin θˆj (D) the rate at which momentum of the ball is changing is constant 17. A particle has initial velocity 10 m/s. It moves due to constant retarding force along the line of velocity which produces a retardation of 5 m/s 2 . Then (A) the maximum displacement in the direction of initial velocity is 10 m (B) the distance travelled in first 3 seconds is 7.5 m (C) the distance travelled in first 3 seconds is 12.5 m (D) the distance travelled in first 3 seconds is 17.5 m