CHAPTER — 4 MOTION IN A PLANE (ULTIPLE CHOICE QUESTIONS 1. Two vectors of the same physical quantity are equal if a. they have same magnitude and the same direction b. they have different magnitudes but same direction, c. they have same magnitude but different directions. 4. they have different magnitude and different directions. ANS: a. Explanation: Property of equal vectors specities its magnitude and direction that for two vectors to be equal, their magnitude and direction should be the same. 2, In the given diagram. R is the resultant of A and B. Then R = B/\2, value of angle 0 is a. 30° b. 45° ©. 60° 4. 75° ANS: b. Explanation: As per the right angled triangle the angle will be 45°. 3. Four bombs of 5 kg, 15 kg, 25 kg and 45 kg are fired from cannon with the same velocity in the same direction. Which of the following options is right___? Note: Ignore air resistance a. All bombs will reach the ground at the same time. b. The time taken will be in direct proportion to their masses. c. The time taken will be inversely proportional to their masses d. The range will not be the same. ANS: a. Explanation: The time of flight does not depend upon the mass. Hence, all bombs will reach the ground in the same time, 4. The motion of a train along a straight railway track is an example for a. two dimensional motion b. one dimensional motionc. three dimensional motion d. motion with uniform speed ANS: b. Explanation: The straight line motion just specifies the distance travelled w.x.t time, 5. If the magnitude of sum of two vectors is equal to magnitude of difference of two vectors, the angle between these two vectors a. 90° b. 180° ©. 360° 0° Explanation; When the magnitude between the vectors sum and difference is equal; the vectors, will lie perpendicular to each other. Hence @ = 90° 6. A car starting from rest at a constant acceleration covers a distance ’s’ in time interval °t’. It covers a distance s; in the next time interval at the same acceleration. The statement which is true is a. S2=S; b.S2=25, ©. $2=3 S81 d.S2=4 8; ANS: c. Explanation: Initial velocity is zero. v =u + at. Therefore, v = at 2 Ssuts 1/2 a? = 12 at? For the next distance covered, u = at - v (from the previous motion) 2 Sy=ut+ 1/2at”=3/2 at” Hence, $2 = 3 S, 7. Veetors ean be added, subtracted and multiplied by a. ordinary laws of algebra b. graphical representation only c. laws of vectors 4. It is not possible to do mathematical operations on vectorsANS: c. Explanation: only laws of vectors is applicable to do vector operations. 8. A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. This implies that its 2 a. acceleration is constant b. velocity is constant c. kinetic energy is variable d. path of movement is circular ANS: d Explanation: A force as mentioned in the question makes the particle move along a circular path at a constant speed. Hence, kinetic energy is constant, But, velocity and acceleration continuously change due to change in direction. 9. A boat moves from a point A (4i+5}) to another point across the river. The new position of the boat is given by B (~7i-9}). The displacement veetor is given by __. a. Hi +14} b. «117 14} “Hi +14} i -14j ANS: a, Explanation: Position A of the boat is given by 4i+5} Position B of the boat is given by —7i-9} ‘We know that the displacement vector At=Axi+Ayj > Ar—= (41+5}) — (-7i-9)) Are 114} 10. A body is projected horizontally from a point above the ground. The motion of the body is given by the equations x = 2t and y = 5t” where x and y are horizontal and vertical displacements in m at time t. The trajectory of the body is__. a. a straight line b.acircle c. an ellipse d.a parabolaANS: d, Explanation: It is given that x = 2t and y = St’. Substituting for tin the equation for y, we get y= (5*x/2) =5x"/4 ive, yor? Therefore, the path is parabolic. 11. Scalar is specified by number and units. Here the number represents its a. Direction b. Magnitude ©. Quantity 4. Location ANS: b, Explanation: Because Scalar has only magnitude. 12. Two trains 121m and 99m in length are running in opposite directions with velocities 40krm/hr and 32km/hr. They will completely cross each other at a. 11 seconds b. 21 seconds c. will not cross at all d.3 seconds ANS: a. Explanation 1,= 121m Ig = 99m Where I, + Ip are lengths of train A and B. Relative velocities of two trains will be Van= Va - Va= 40 - (-32) = 72 km/hr = 20m/s. Total distance travelled = 121 + 99 = 220 m. Therefore, Time = 220/20 = 11 see 13. If the quantity, position of a particle is represented using + and - signs then, the posi is being expressed in a. one dimension b. two dimension c. three dimension4. first the integers are in use ANS: d. Explanation: The signs indicate just the position of the place 14. A particle moves with a constant speed v along a circular path of radius r and completes the circle in time T. The acceleration of the particle is__- a, 2an/T . avi c.2nr/T @.2nv'/T ANS: b. Explanation: For circular motion, v= 2nr/T =r = vT/2n Acceleration a=v"/t=v"/ (vT/2n) = 2xv/T 15. A particle is given a displacement of 4m in the x - y plane. If the x component of. displacement vector is 2m, then y component is: a.2m b.2V2m ©. 23m 4.4m ANS: c Explanation: D? = Dx’ + Dy’ (4) =(2)° + Dy* Therefore, Dy*= 4*- 2? = 16-4 = 12m Dy = V12 = V4 «V3 =2 V3m. 16. The magnitude of the resultant of two equal vectors is equal to the magnitude of either vector, Then the angle between the two vectors a. 150° b. 120° ©. 90° d. 60° ANS: b.Explanation: Because the magnitude of resultant vector is equal to the magnitude of given two vector (ie.) R =A=B If the two vectors are inclined at an angle '0' then, R? = A? + B? + 2AB cos. (Because RA 2ABcos6....) A’ = A? + B’ + 2A? cos6) A’ =2A + 2A? cos 1=2(1 + cos0) 2+2cosd=1 2 e080 = cos0=—1/2=120° 17. Veetors which are having equal or unequal magnitudes and are acting along parallel straight lines are, a. coplanar vectors b. collinear vectors ¢. co-initial vectors 4. localised vectors ANS: b. Explanation: As per the definition of collinear vectors. 18. Zero vector or null vector is a necessity because, a. Zero as a number should be used b. There are no such zero vectors, itis only a scalar. c. When two vectors are equal, the resultant should be a vanishing vector with arbitrary direction. 4. Ithelps in the dot product of two scalars. ANS: Explanation: For any vector calculation, vector cannot be nullified and hence there should be zero vector, 19. If number of vectors is represented in magnitude and direction by the sides of a polygon taken in same order, then their resultant is represented in magnitude and direction by? a. any one of the given vector but in opposite order b. the closing side of the polygon taken in opposite order c. the line joining any two vertex of the sides d. cannot be represented in polygon ANS: b.Explanation: Itis as per the polygon law of vectors addition which states that the resultant vector should be the closing side of polygon, but the direction will be opposite. 20. A man is at a distance of 6m behind a bus. The bus begins to move with a constant acceleration of 3 m/s’. In order to catch the bus the minimum speed with which the man should run towards the bus is a.2mi/s b.4mis ©. 6 mis a. 8 m/s ANS: c. Explanation: Let us assume that the man will catch the bus after ’t’ seconds. Then, the distance that the bus would have travelled will be Distance travelled by the man is S = vt To catch the bus, the passenger should cover the distance $1 st=ve Wv2adya 't' can be real only if v 2 V2ad Therefore, the minimum speed that the man should run will be V2ad m/s = \ (2 x 3 x 6) = 6 mis. 21. At 10 am, the position of an aircraft relative to an airport O is (220i + 50j) km, i and j being unit vectors due east and due north respectively. The velocity of the aireraft is (150i - 100j) km/hr. At 11 am, the aircraft will be at___ from the airport. a. 450km b. 399.25 km c. 373.86 km 4,373.36 km ANS: d Explanation: It is given that at 10 am, the position of an aircraft relative to an airport O is (220i +50j)km. The velocity of the aircraft is (150i - 100)) knw/hr. Hence, in one hour, the displacement of the aircraft is (150i - 100j) km. The new position is (220i + 50j) + (150i - 100j) = 370i - 50) km from the airport. Distance of the aircraft from the airport = \(3707+50°)=373.36km. 22, If the direction of a vector is along the axis of rotation, then the vector indicates anticlockwise or clockwise___. a. rotational effect,b. straight line effect c. parallel effect 4. perpendicular effect ANS: a. Explanation: This is as per the definition of rotational effect. 23. A man stands at a distance ’d’ m behind a bus which moves forward with a constant acceleration ‘a’, He starts running at a constant speed 'v' m/s. The minimum speed of the passenger so that he can catch the bus is a. 2ad m/s b. V(2ad)m/s ©. ad/2 mis dad m/s ANS: a. Explanation: Let us assume that the man will catch the bus after ’t” second: Then, the distance that the bus would have travelled will be S Distance travelled by the man is S> = vt To catch the bus, the passenger should cover the distance S; + d= So, d+ 1/2 at®= vist = (vi Vv?-2ad)/(a) 't' can be real only if v > V2ad Therefore, the minimum speed that the man should run will be V(2ad) m/s at” 24, Two parallel rail tracks run from North to South. On one track, train A is moving from South to North with a speed of 20 m/s. On the other track, train B is moving from North to South with a speed of 30 mis. The relative velocity of A with respect to Bis. a. 50 m/s in the direction - South to North b. 50 mis in the direction - North to South c. 10 m/s in the direction - South to North 4. 10 mis in the direction - North to South ANS: a. Explanation: Let us consider the track to be along the Y-axis. Then Va = 20 m/s and Vp =-30 mis. Relative velocity of A with respect to B is Van = Va~ Vn = 20 - (-30) = 50 mis (South to North) The angle between A i4jand B=i-jis25. (a) 45° (b) 90° (c) 45° (a) 180° ANS: (b) 26. For two veetors A and B, |A + B|=|A —B] is always true when (a) |Al= Bl#0 (ALL BI (©) |AI=[B] #0 and A and B are parallel or anti parallel (d) when either [AJ or [B] is zero. ANS: (b), (@) 27. For a particle performing uniform circular motion, choose the correct statement(s) from the following: (a) Magnitude of particle velocity (speed) remains constant, (b) Particle velocity remains directed perpendicular to radius vector. (©) Direction of acceleration keeps changing as particle moves (d) Angular momentum is constant in magnitude but direction keeps changing. ANS: (a), (b), (©) 28. The component of a vector r along X-axis will have maximum value if (a) ris along positive Y-axis (b) r is along positive X-axis (c) rmakes an angle of 45° with the X-axis (d) ris along negative Y-axis ANS: (b) 29. The horizontal range of a projectile fired at an angle of 15° is 50 m. If it is fired with the same speed at an angle of 45°, its range will be (a) 60m (6) 71m(©) 100m (d) 141m ANS: (c) 30. It is found that |A+BI-/A\. This necessarily implies, (a) B=0 (b) A,B are antiparallel (c) A,B are perpendicular (@ABS0 ANS: (b) 31.If the resultant of n forces of different magnitudes acting at a point is zero, then the minimum value of n is A) 1 B) 2 ° 3 D) 4 Answer ¢ 32.Can the resultant of 2 vectors be zero A) Yes, when the 2 vectors are same in magnitude and direction B) No. ° Yes, when the 2 vectors are same in magnitude but opposite in sense D) Yes, when the 2 vectors are same in magnitude making an angle of 2n/3 with each other ans: ¢ 33.The sum of the magnitudes of two forces acting at point is 18 and the magnitude of their resultant is 12. If the resultant is at 90° with the force of smaller magnitude, what are the, magnitudes of forces A) 12,5 B) 14,4 c) 5,13D) ans: ¢ 10,8