PART TEST-1 DATE:13-02-2021 NEET-2021 MOTION IN A PLANE 1. A projectile starts with speed u at an angle θ from 5. A particle of mass 6 kg moves with an initial velocity of the horizontal ground. The average velocity of the → ˆ ˆ v = (8 i + 8 j) m/s. A constant force of projectile between the point of projection and the point of → arrival on the ground is: ˆ F = − 30 j N is applied to the particle. Initially, the particle was at (0, 0). The x-coordinate of the particle, (1) usinθ when its y-coordinate again becomes zero is given by (2) 2usinθ (1) 6.0 m (3) ucosθ (2) 12.8 m (4) 2ucosθ (3) 8 m (4) 25.6 m 2. The trajectory of a projectile in the vertical plane is y = 6. A projectile is projected with speed u at an angle of 30° ax - bx where a and b are constants, x and y are with the vertical from the ground. The angle between the horizontal and vertical displacements from point of acceleration of the projectile and its velocity at the time projection. The angle of projection from the horizontal is of striking the horizontal ground is: 2 1. tan 2. tan 3. tan 4. tan −1 ( a b (1) 30° ) (2) 60° −1 (b) (3) 45° −1 ( −1 b a ) (4) 0° (a) 7. A missile is fired for maximum range with an initial velocity of 20 m/s, then the maximum height of 3. A particle is thrown horizontally from a pole of height missile is 500 m with an initial speed of 50 m/s. The distance between the foot of the pole and striking point of the (1) 20 m particle on the ground is: (g = 10 m/s ) (2) 30 m (1) 100 m (3) 10 m (2) 250 m (4) 40 m (3) 500 m 2 (4) 1000 m 8. Two projectiles projected with the same speed at angles θ and (90° - θ) from the same point, then H × H is equal to (where symbols have their usual meanings) 1 4. Two balls are projected to acquire same range with the same initial speed u but at different angles of projection. If maximum height acquired by balls are H and H , then (H + H ) is: (angle of projection of one projectile is θ) 1 2 (1) tan (2) cot (3) u 2 2 2 2g θ θ 1 2 1. R 2. R 2 2 3. 16 4. 2 R 2 8 9. A particle is moving eastwards with velocity of 5 m/s. In 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is1. Zero 2. (4) tan θ 3. 4. 1 m/s 2 √2 1 m/s √2 1 2 m/s 2 2 toward north-west toward north-east toward north-west Page: 1 2. 50 J 10. If horizontal range of a projectile is 4√3 times its maximum height. Its range of projection will be 3. 75 J 4. 0 J 1. 45° 2. 60° 14. The equation of trajectory of a projectile given angular projection is y = ax - bx2, then horizontal range of projectile is 3. 90° 4. 30° 1. 11. A stone is pfojected with a velocity v at an angle θ with the horizontal reaches maximum height H1. When it is 2. with the horizontal, 3. it reaches maximum height H2. The ratio between hrizontal range R of the projection, H1 and H2 is ? 4. projected with u at an angle ( 1. R = 2√ H 1 H 2 2. R = √ H1 H2 3. R = 4√ H 1 H 2 4. R = π 2 − θ) a b a 2b 2a b a 4b 15. A large number of bullets are fired in all directions with same velocity u. What is the maximum area on the ground on which these bullets can spread ? πu 2. πu 3. π u 4. π u 8√ H 1 H 2 12. The velocity of a projectile at the initial point A is ˆ ˆ (4 i + 5 j) m/s. Its velocity in m/s at point B is 2 1. g g 4 2 2 g 2 g 4 2 2 2 16. A particle is thown with a speed u at an angle θ with the horizontal. When the particle makes an angle ϕ with the horizontal, its speed changes to v, Which is equal to 1. (4ˆi + 5ˆj) 4. (4ˆi − 5ˆj) cos θ 2. u cos θ cos ϕ 3. u cos θ sec ϕ 4. u sec θ 2. (−4ˆi − 5ˆj) 3. (−4ˆi + 5ˆj) 1. u cos ϕ 17. A smooth square platform ABCD is moving towards right with uniform speed u. At what angle θ must a particle be projected from A with speed v, so that it strikes the point D ? 13. A body is projected with initial kinetic energy of 100 J and at an angle of 60° with the horizontal. The K.E. of the body at highest point will be 1. 25 J Page: 2 1. sin −1 2. cos 3. sin −1 −1 4. cos ( ( ( −1 ( 18. u v v u v u u v ) ) ) ) 1. 45 0 2. 60 0 3. 30 0 4. None 20. The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by y = 8t − 5t m and x = 6t m, where t is in seconds. The velocity with Time taken by the projectile to reach from P to Q is t, which the particle is projected is. then PQ ? 2 1. 2ut 1. 14 m/s 2. √3 ut 2. 10 m/s 3. √3 4. ut 2 3. 8 m/s ut 4. 6 m/s √3 21. A particle of mass m is projectile with a velocity v 19. A aeroplane moving with a speed of 250m/s is at a height making an angle of 30 with the horizontal. The of 6000 m just overhead of an ant, aircraft gun. Muzzle magnitude of angular momentum of the projectile about the point of the projection when particle is at it's speed of shell is 500m/s, the firing angle θ should be ? maximum height h is o 1. √ 3 mv 2 g 2 2. zero 3. mv 3 √2g √3 4. 16 mv 3 g 22. if a person can through a stone to maximum height of h meter vertically, then maximum distance Page: 3 through which it can be thrown horizontally by the same person is 1. h/2 3. 1440 m 4. 960 m 27. 2. h A cart is moving horizontally along a straight line with contant speed of 30 m/s. A projectile is to be fired from the moving cart in such a way that it will return to the cart after the cart has moved 80 m. At what speed (relative to the cart) must the projectile be fired ? (given g = 10 m/s2) 3. 2h 4. 3h 23. At the top of the trajectory of a projectile, direction of its velocity and acceleration are 1. perpendicular to each other 1. 10 m/s 2. 40 3 m/s 3. 10√8 m/s 2. parallel to each other 4. None of the above 3. inclined to each other at angle of 45 0 28. 4. antiparallel to each other 24. At the height 80 m an aeroplane is moving with 150m/s. A bomb is dropped from it, so as to hit a target. At what distance from the target should bomb be dropped ? A cart is moving with speed of 20m/s on a horizontal track. A body is projected with speed 40m/s (relative to cart ) from the cart in such a way that path of body appear to be straight line for an observer on ground. Time for which body remains in air is: 1. 2√3 sec 1. 605.3 m 2. 4 sec 2. 600 m 3. 4√3 sec 3. 80 m 4. 8 sec 4. 230 m 25. 29. Three balls are dropped from the top of a building with A body is projected with speed u at an angle θ with the equal speed at different angles. When the balls horizontal after what time it will start moving perpendicular to its initial direction of projection. strike ground, their velocities are v , v & v respectively , than 1. t = 1 2 3 u g sin 2θ 1. v1 > v2 > v3 2. v3 > v2 > 3. v1 = 4. v1 < v2 v2 = v1 v3 2. t = 3. t = 4. t = < v3 26. An object of mass 2m is projected with a speed of 100 m/s at an angle θ = sin −1 ( 3 5 ) to the horizontal. At the 2u g sin θ u 2g sin θ u g sin θ 30. Galileo writes that for angles of projection of highest point, the object breaks into pieces of same mass m & the first one comes to rest . The distance between point of landing of the bigger piece is (given g = 10 m/s2 ) 1. 3840 m 2. 1280 m Page: 4 31. A particle is projected at an angle θ with horizontal with an initital speed u. When it makes an angle α with horizontal, its speed v is1. u cos θ 3. 4. u cos θ 1. u cos θ 2. u tan θ 2. u cos θ u cos α u sin θ A particle is projected with a velocity u making an angle θ with the horizontal. At any instant, its velocity v is at right angles to its initial velocity u; then v is: 3. u cot θ 4. u sec θ sin α 36. cos α A projectile is given an initial velocity of ˆi + 2ˆj . The cartesian equation of its path is (g = 10 ms ) −2 32. A body is projected with velocity 20√3 m/s with an angle of projection 60° with horizontal. Calculate velocity on that point where body makes an angle 30° with the horizontal. 20 2. y = x − 5x 2 2 3. 4y = 2x − 5x 4. y = 2x − 25x 1. 20 m/s 2. 1. y = 2x − 5x 2 2 37. m/s √3 A ship A is moving westwards with a speed of 10 km h and a ship B, 100 km south of A is moving northwards with a speed of 10 km h . The time after which the distance between them becomes the shortest, is: 3. 10√3 m/s −1 −1 4. 10 m/s 33. A particle is moving with veocity ⇀ ˆ ˆ V = k(y i + x j) ; 1. 5 hr where k is constant. The general equation for path is: 2. 5√2 hr 1. y = x 3. 10√2 hr 2. y 2 2 = x + constant 2 + constant 3. y = x + constant 4. xy=constant 4. 0 hr 38. Time taken by the projectile to reach from A to B is t. Then the distance AB is equal to : 34. A body thrown vertically so as to reach its maximum height in t second. The total time from the time of projection to reach a point at half of its maximum height while returning (in second) is: 1. √2t 2. (1 + 3. 3t 4. t 2 √2 1. 1 √2 ut √3 )t 2. √3ut 2 3. √3ut 4. 2ut 35. Page: 5 39. horizontal. Which of the following statements is correct . The height y and the distance x along the horizontal plane of a projectile on a certain planet (with no surrounding atmosphere) are given by y = 8t − 5t m and x = 6t m, where t is in seconds. The velocity with which the particle is projected is. 2 3. Range of A and C are equal & greater than that of B 44. 2. 10 m/s At the height 80 m an aeroplane is moving with 150m/s. A bomb is dropped from it, so as to hit a target. At what distance from the target should bomb be dropped ? 3. 8 m/s 4. 6 m/s 40. 1. 605.3 m A particle of mass m is projectile with a velocity v making an angle of 30 with the horizontal. The magnitude of angular momentum of the projectile about the point of the projection when particle is at it's maximum height h is o 1. √ 3 mv 2 mv 3. 80 m 4. 230 m 45. Three balls are dropped from the top of a building with equal speed at different angles. When the balls strike ground, their velocities are v , v & v respectively , than g 3 1 √2g √3 2. 600 m 2 2. zero 4. 2. Range of A and C are less than that of B 4. A, B and C have equal ranges 1. 14 m/s 3. 1. A, B and C have unequal ranges mv 3 3 1. v1 > v2 > v3 g 16 2 41. 2. v3 > v2 > 3. v1 = v2 = v1 v3 if a person can through a stone to maximum height of h 4. v < v < v meter vertically, then maximum distance through which 46. it can be thrown horizontally by the same person is An object of mass 2m is projected with a speed of 100 1. h/2 m/s at an angle θ = sin ( ) to the horizontal. At the 2. h highest point, the object breaks into pieces of same mass 3. 2h m & the first one comes to rest . The distance between point of landing of the bigger piece is (given g = 10 m/s2 4. 3h ) 1 2 3 −1 3 5 1. 3840 m 42. At the top of the trajectory of a projectile, direction of its velocity and acceleration are 3. 1440 m 4. 960 m 1. perpendicular to each other 2. parallel to each other 3. inclined to each other at angle of 45 2. 1280 m ******* 0 4. antiparallel to each other 43. These particles A, B and C are projected from the same pair with same initial speed making angles 30 45 & 60 respectively with the o, o o Page: 6