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FOR CBSE MAINS
Motion in One, Two and Three Dimension

 

Question (1 mark)

 

Q1.       Is it possible that a body can be treated simultaneously at rest as will as in motion?

 

Ans.     Rest and motion are relative terms. A person sitting in a moving bus is at rest with reference to the frame of the bus but in motion with reference to the outside buildings, trees or poles.

 

Q2.       A car moves at uniform speed of 60 km h-1 on straight road blocked by a wall. The jeep has to take a sharp perpendicular turn along the wall. A fly rocket at uniform speed of 100 km h starts from the wall towards the jeep when jeep is 30 km away. The fly rocket reaches the windscreen and returns to wall. What is the told distance covered by fly rocket?

 

Ans.     Time taken by car to cover a distance of 30 km=

                                                                       

                                                                       

 

Total distance covered by fly rocket in this duration = 100 ´ ˝ = 50 km

 

Q3.       What is represented by the area under a velocity time graph?

 

Ans.     The velocities at different instants can he plotted as shown in the figure. The graph here shows uniform velocity.

 

 

or distance, s =  v x t.

Thus area under a velocity time graph gives displacement.

 

Q4.       Pick the one dimensional motion

(i) A bird flying here and there is sky

(ii) Motion of a communication satellite around earth.

(iii) Rebounding of striker of a carom board.

(iv) Truck running on straight road.

 

Ans.     Truck running on a straight road is an example of one dimensional motion because in this case motion is kept along a straight line.

 

Q5.       It is correct to say that a speedometer measures average speed?

 

Ans.     No, a speedometer indicates instantaneous speed only.

 

Q6.       Give ratio of speed to velocity of a moving object.

 

Ans.     Velocity can be less than or equal to speed

 

           

           

Q7.       Can an object have?

(i) Constant speed bur variable velocity

(ii) Constant velocity but varying speed.

 

Ann.     (i) Yes, eg. Uniform circular motion

(ii). No, because constant velocity means that both magnitude and direction of velocity are fixed. Magnitude of velocity can be taken as speed so in this case speed is also fixed.

 

Q8.       Can time be taken as negative?

 

Ans.     Yes, positive and negative are simply relative terms. If we take the instantaneous time before the origin i.e. zero consideration of time then it can be taken as negative.

 

Q9.       Can a body have zero velocity and finite acceleration or can a particle in one dimension motion with zero speed at any instant may have not zero acceleration at that instant.

 

Ans.     Yes, a body can have non zero acceleration at any instant when speed is zero. If a ball is thrown vertically up it has zero velocity at the top moxt point and non zero acceleration due to gravity, g = 9.8 ms-2

 

Q10.     If a body has constant speed, is he true that it can have acceleration?

 

Ans.     Yes, an object moving along a circular path with constant speed has acceleration due to continuous change in direction.

 

Q11.     A particle is one dimensional motion with positive value of acceleration must be speeding up’. Do you agree with this statement?

 

Ans.     It is a false statement because in the case of initial velocity of a particle being negative, the particle speeds down even if the acceleration is positive.

 

Q12.     Is the acceleration of an automobile greater when brakes are applied hard or when the accelerator is given?

 

Ans.     In the first case the acceleration is greater because the car is suddenly stopped so the rate of change of velocity i.e. acceleration is large.

 

Q13.     One light and another heavy mass are thrown vertically upwards with some initial speed. Which one will attain higher height?

 

Ans.     The height attained is independent of the mass of body so with same initial speeds both will attain same height.

 

Q14.     If a body has no acceleration when if is moving with uniform velocity in a straight line, will it be in equilibrium?

 

Ans.     Yes, it is in equilibrium because for equilibrium the next force should be zero i.e., net acceleration should be zero.

 

Q15.     Why does a parachute descend slowly?

 

Ans.     Due to retardation.

 

 

Question (2 marks)

 

Q1.       What do you understand by static’s, dynamics and kinematics?

 

Ans.     Static’s is a branch of mechanics which deals with the study of rest conditions of a body.

Dynamics is a branch of mechanics which deals with the study of motion of objects taking into account the cause of motion.

Kinematics is a branch of mechanics which deals with the study of motion of objects without taking into account the cause of motion.

 

Q2.       In which of these cases a body can be considered as point object:

(a)     a train moving without jerks between two stations.

Ans.     Since the motion of the train between two distant stations is smooth throughout so keeping in view the long distance covered between the two stations in reasonable duration of time, the size of the train is neglected and it is considered as a point object.

 

(b) A monkey sitting on top of a man cycling smoothly on a circular track.

Ans.     The distance covered by the monkey in reasonable duration of time is more so tit is considered as a point object.

 

(c) A spinning cricket ball turns sharply on hitting the ground.

Ans.     Since the turning of the ball is not smooth but sharp so the distance covered by it in reasonable duration of time is not large so this ball can not be treated as a point object.

 

 

            (d) A tumbling beaker slipped off the edge of a table.

Ans.     Since the beaker is tumbling and then slipls off so the distance covered by it in reasonable duration of time is not large so it is not treated as a point object.

 

(e) Earth revolving around sun.

Ans.     Size of earth is too small as compared to radius of orbit around sun so it can be treated as a point object.

 

Q3.       The position time (x-t) graphs for two children A and B returning from their school O to their homes P and Q respectively are shown. Choose the correct entries:

 

(a) (A/B) lives closer to the school than (B/A)

Ans.     A lives closer to the school than B because B has to cover higher distance [OP< OQ]

 

(b) (A/B) starts from the school earlier than (B/A)

Ans.     A starts from the school earliest than B because t = 0 for A but B has some finite time.

 

(c) (A/B) walks faster the (B/A)

Ans.     B walks faster than A because it covers more distance in less duration of time [slope of B is greater than that of A)

 

(d) A and B reach home at the (same/ different) time

Ans.     A and B reach home at the same time.

 

(e) (A/B) overtakes (B/A) on the road (one/ twice)

 

Ans.     B overtakes A on the road once (at X i.e. the point of intersection.)

 

Q4.       State with reasons which of these cannot possibly represent one dimensional motion of a particle.

 

                    

            

Ans.     Figure (a) does not represent one dimensional motion of particle because the particle has two different positions at the same instant which is not the case of one dimensional motion. Figure (b) also does not represent one dimensional motion of the particle because here the total path length is shown to decrease with time which is not possible in one dimensional motion.

 

Q5.       What is instantaneous velocity?

 

Ans.     The velocity of a body at a particular position or instant is called instantaneous velocity.

It is defined as the limit of the average velocity of a body when time interval D t becomes infinitesimally small i.e.

 

 

Thus instantaneous velocity is the rate of change of position of a moving body with respect to time at that instant.

 

Q6.       A man standing on the edge of a cliff throws a store straight down with same initial speed u and then throws another stone straight up with initial speed u and from the same position. Find ratios of speeds, two stones would attain, when they hit ground at the base of the cliff.

 

Ans.     The stone thrown upward reaches back to the thrown with speed u.

Thus both the stones fall under the influence of gravity with same initial velocity u so the two stones will hit the ground with same speed. Hence ratio of their speeds when they hit ground is 1.

 

Q7.       Is variation of time possible with position as shown?

 

           

 

Ans.     No, because from B to C position changes from x1 to x2 on positive direction but time is shown to be reduced (t1 to zero) which is not possible.

 

Q8.       Can an object have

(i) constant speed but variable velocity

Ans.     (i) Yes, e.g uniform circular motion.

 

(ii) constant velocity but varying speed.

Ans.     No, because constant velocity means that both magnitude and direction of velocity are fixed. Magnitude of velocity can be taken as speed so in this case speed is also fixed.

 

Q9.       Give conditions when

(i) magnitude of displacement = distance

Ans.     In case an object is having uniform motion in a straight line.

 

(ii) magnitude of average velocity = speed

Ans.     In case an object is having uniform motion along a straight line.

 

(iii) average velocity = instantaneous velocity.

Ans.     In case an object is having uniform motion in one dimension.

 

Q10.     Displacement of a body is given by a sin (vt + f) where a is amplitude, v is angular velocity, t is time and f is phase difference. Find time for maximum displacement.

 

Ans.     For maximum displacement sin (wt + f) should be unity

 

i.e. (wt + f) = p/2         i.e. wt = p/2 - f

 

           

 

Question (3 marks)

 

Q1.       Suggest a physical situation for the following graphs?

           

 

Ans.     Graph (a) may represent a particle lying at rest on a smooth floor gets a kick to strike a wall. It then rebounds to strike the opposite wall which ultimately stops it because the graph indicates increased in distance with time then decrease in distance with time leading to reversal of direction and then constant distance throughout.

Graph (b) may represent the repeated bouncing of a particle which hits the floor and rebounds in hit the floor again because the graph indicates repeated continuous drop in velocity with time followed with reversal in the directions.

Graphs (c) may represent a particle moving with uniform velocity hit for a very short duration in the opposite direction because the graph shows the acceleration for a very short time interval.

 

Q2.       A driver driving a truck at constant speed of 20 ms-1 suddenly saw a parked car ahead of him by 95m. He could apply the brake after some time to produce retardation of 2.5 ms-2. What is his reaction time when accident is just avoided?

Ans.     Let the driver apply the brakes at y then

S1= 20 ´ t

Using 2as= v2-u2, we get,

2 (-2.5) s2 = 0 - 202                    ( because of retardation)

But 95 = s1 + s2

Or s1 = 95 – s2= 95 – 80 = 15m

From (i), t = s1/20 = 15/20 = 0.75s.

 

Q3        A small ball rolls down a staircase with uniform horizontal velocity u. If each step is y m high and x m wide, the marble just hits the edge of the nth step. Find the value of n.

Ans.     Total horizontal distance to be covered

            = x x n = nx

            Total vertical distance to be covered

            = y x n = n

            but nx = ut

            (using s = ut + ˝ at2)                 (1)

 

           

 

            and

            Substituting the value of t from equation (i) in equation (ii)

 

           

 

Q4.       A police van moving on a highway with a speed of 30 kmh-1 fires a bullet a thief’s car speeding away in the same direction with a speed of 192 km h-1. If the muzzle speed of the bullet is 150 ms-1, with what speed does the bullet hits the thief’s car?

 

Ans.     Here velocity of police van (uv), muzzie velocity of bullet (vb) and velocity of car (vc) are all in the same direction.

 

           

 

            vb= 150 ms-1 and vc = 192 km/h-1

 

            Effective velocity of bullet

 

           

           

            Relative velocity of bullet w.r.t. car,

 

           

 

            = 105 ms-1

 

 

 

Objective Questions based on
Motion in Two and Three Dimension

 

 

Q1.       A particle is projected with a velocity v, so that its range on a horizontal plane is twice the greatest height attained. If g is acceleration due to gravity, then its range is:

(a) 4v2/5g          (b) 4g/5v2          (c) 4v3/5g2         (d) 4v/5g2

 

Ans.     (a)

 

Q2.       During a projectile motion if the maximum height equals the horizontal range, then the angel of projection with the horizontal is

(a) tan-1 (1)        (b) tan-1 (2)                    (c) tan-1(3)                     (d) tan –1 (4)

 

Ans.     (d)

 

Q3.       The point from where a ball is projected is taken as the origin of the coordinate axes. The x and y components of its displacement are given by x = 6t and y = 8t – 5t2. What is the velocity of projection?

(a) 6 ms-1          (b) 8 ms-1          (c) 10 ms-1        (d) 14 ms-1

 

Ans.     (c)

 

Q4.       A particle is fired with velocity u making angle q with the horizontal. What is the change in velocity it is at the highest point?

(a) u cosq         (b) u     (c) u sinq          (d) (u cosq - u)

 

Ans.     (c)

 

Q5.       In the Q.4. the change is speed is

(a) u cosq         (b) u     (c) u sinq          (d) (u cosq - u)

 

Ans.     (d)

 

Q6.       A ball whose kinetic energy is E, is thrown at an angle of 450 with the horizontal, its kinetic energy at the highest point of its flight will be.

(a)  E

 

 

 

(d) zero

 

Ans.     (c)

 

Q7.       Two bullets are fired horizontally with different velocities from the same height. Which will reach the ground firs?

(a) Slower one

(b) Faster one

(c) Both will reach simultaneously

(d) It cannot be predicted

 

Ans.     (c)

 

Q8.       A ball is thrown upwards and it returns to ground describing a parabolic path. Which of the following quantities remains constant throughout the motion?

(a)     Kinetic energy of the ball

(b)    Speed of the ball

(c)     Horizontal component of velocity

(d)    Vertical component of velocity

 

Ans.     (c)

 

Q9.       An aero plane moving horizontally with a speed of 180 km/hr drops a food packet while flying as a height of 490 m. The horizontal range is:

(a) 180 m          (b) 980 m          (c) 500 m          (d) 670 m

 

Ans.     (c)

 

Q10.     The range of a rifle bullet on level ground is 6000 m. The range at an incline of 300 is

(a) 4000 m         (b) 2000 m        (c) 6000 m         (d) 1000 m

 

Ans.     (a)

 

Q11.     The maximum height attained by a projectile is increased by 10% keeping the angle of projection constant, what is percentage increase in the time of flight?

(a) 5%   (b) 10%             (c) 20%             (c) 40%

 

Ans.     (a)

 

Q12.     If the time of flight of a projectile is doubled, what happens to the maximum height attained?

(a) Halved         (b) Remains unchanged             (c) Doubled       (d) Becomes four times

 

Ans.     (d)

 

Q13.     A body of mass 2 kg has an initial velocity of 3 m/s along x-axis and it is subjected to a force of 4N in y-direction. The distance of the body from origin after 4 seconds will be: (the body was subjected to force at the origin at t=0)

(a) 12 m            (b) 28 m            (c) 20 m            (d) 48 m

 

Ans.     (c)

 

Q14.     A body has an initial velocity of 3 m/s and has an acceleration of 1 m/sec.2 normal to the direction of the initial velocity. Then its velocity 4 seconds after the start is:

(a)     7 m/sec along the direction of initial velocity

(b)    7 m/sec along the normal to the direction of initial velocity

(c)     7 m/sec mid – way between the two directions

(d)    5 m/sec at an angle of tan-1 (4/3) with the direction of initial velocity.

 

Ans.     (d)

 

Q15.     A person can throw a stone to a maximum height of h metre. The maximum distance to which he can throw the stone is:

(a) h      (b) h/2    (c) 2h    (d) 3h

 

Ans.     (c)

 

Q16.     An arrow is shot into the air Its range is 2000 metres and its time of flight is 5 sec. If the value of g is assumed to be 10 m/sec2, then horizontal component of the velocity of arrow is:

(a) 25 m/s         (b) 40 m/s         (c) 31.25 m/s     (d) 12.5 m/s

 

Ans.     (b)

 

Q17.     In the Q. 16, the maximum height attained by the arrow is:

(a) 12.5 m         (b) 25 m            (c) 31.25 m        (d) 40 m

 

Ans.     (c)

 

Q18.     In the Q. 16, the vertical component of the velocity is:

            (a) 12.5 m/s

            (b) 31.25 m/s

            (c) 25 m/s

            (d) 40 m/s

 

Ans.     (c)

              

Q19.     In the Q. 16, the angle of projection with the horizontal is

 

           

           

              

 

           

 

           

 

Ans.     (c)

 

Q20.     The ceiling of a hall is 40 m high. For maximum horizontal distance, the angle at which the ball may be thrown with a speed of 56 ms-1 without hitting the ceiling of the hall is:

(a)     250

(b)    300

(c)     450

(d)    600

 

Ans.     (b)

 

Q21.     From the top of a tower 19.6 m high, a ball is thrown horizontally. If the line joining the point of projection to the point where it hits the ground makes and angle of 450 with the horizontal, then the initial velocity of the ball is:

(a)     9.8 ms-1

(b)    4.9 ms-1

(c)     14.7 ms-1

(d)    2.8 ms-1

           

Ans.     (a)

 

Q22.     Two tall buildings are 30 m apart. The speed with which a ball must be thrown horizontally from a window. 150 m above the ground in one building so that it enters a window 27.5 m from the ground in the other building is:

(a)     2 ms -1

(b)    6 ms-1

(c)     4 ms-1

(d)    8 ms-1

 

Ans.     (b)

 

Q23.     A projectile will cover the maximum vertical distance in the minimum time when the angle of projection with vertical is

(a)     00

(b)    300

(c)     600

(d)    900

 

Ans.     ( a)

 

Q24.     Two paper screens A and B are separated by 150 m. A bullet pierces A and then B. The hole in B is 15 cm below the hole in A. If the bullet is traveling horizontally at the time of hitting A, then the velocity of the bullet at A is.

 

           

           

 

 

           

Ans.     (d)

 

Q25.     The range of a projectile when fixed at 750 with the horizontal is 0.5 km. What will be its range when it is fired at an angle of 450?

(a)     0.5 km

(b)    1.0 km

(c)     1.5 km

(d)    2.0 km

 

Ans.     (b)

 

Q26.     The time of flight of a projection on an upward inclined plane depends upon:

(a)     angle of projection

(b)    angle of inclination of the plane.

(c)     Air resistance

(d)    (a) and (b) both

 

Ans.     (d)

 

Q27.     Which of the following is larges, when the height attained by the projectile is the largest?

(a)     Range

(b)    Time of flight

(c)     Angle of projectile with vertical

(d)    None of above

 

Ans.     (b)

 

Q28.     A body of mass m is projected horizontally with a velocity v from the top of a tower of height h and it reaches the ground at a distance x from the foot of the tower. If a second body of mass 2m is projected horizontally from the top of a tower of height 2h, it reaches the ground at a distance 2x from the foot of the tower. The horizontal velocity of the second body is:

 

(a) v

 

(b) 2v

           

             

 

           

 

Ans.     (c)

 

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