Kinematics Questions and Answers

Q14 A bomb of mass m is projected from the ground with speed v at angle 0 with the horizontal At the maximum height from the ground it explodes into two fragments of equal mass If one fragment comes to rest immediately after explosion then the horizontal range of centre of mass is a b c v sin 0 9 v sine v sine 2g

a 4 tan 0 75 IB me ged to d 143 A river is 1km wide The banks are straight and parallel The current is 5km h and is parallel to the banks A boat has a maximum speed of 3km h in still water In what direction should the boat head so as to arrive at the point B directly opposite to its starting point A 1 Directly across the river 2 Head 53 upstream from the line AB 3 Head 37 upstream from the line AB 4 The trip from A to B is not possible with this speed 144 A force F is given in terms of time t as F AsinCt

9 Figure 9 E11 shows a small block of mass m which is started with a speed v on the horizontal part of the bigger block of mass M placed on a horizontal floor The curved part of the surface shown is semicircular All the surfaces are frictionless Find the speed of the bigger block when the smaller block reaches the point A of the surface A VA m

19 A bird B in air is diving vertically downwards over a water tank with speed 5 cm s Base of tank is silvered A fish F in the tank is rising vertically upwards along the same line with 2 cm s Water level is lowered at the rate of 2 cm s Take Mwater 4 3 5 cm s Match the following two columns Column I 2 cm s 2 cm s Column II p 4 q 8 A Speed of image of fish as seen by the bird directly in cm s B Speed of image of fish formed after reflection in the mirror as seen by the bird in cm s C Speed of image of bird as seen by the fish looking upwards in cm s r 3 Speed of image of bird as seen by the fish looking downwards in cm s s 6

Objective Type Questions The position coordinates of a projectile thrown fro ground are given by y 3t 5t2 m and x 4t r here t is in second x is horizontal and y is vertic horizontal range of the projectile is 1 2 4 m 2 4 8 m 3 9 6 m 4 4 2 m

22 A combination of two identical bar magnets are placed one over the other such that they are perpendicular and bisect each other The time period of oscilla tion in a horizontal magnetic field is 24 seconds One of the magnets is removed and if the other magnet oscillates in the same field then the time period in seconds is 1 21 4 2 21 2 3 2 4 254

A projectile is fired at angle with horizontal with initial speed u If it breaks into two halves such that one half retraces its path then the distance of hitting point of the other half from starting point is 1 2 3 4 u sin 20 g 2u sin 20 g u sin 20 2g u sine 2g

Q2 A bus is moving on a straight road towards north with a uniform speed of 50 km hr then it turns left through 90 If the speed remains unchanged after turning the increase in the velocity of bus in the turning process is a 70 7 km hr along direction b zero c 50 km hr along west along d 70 7 km hr direction south west north west

A ball of mass m is dropped onto a floor from a certain height The collision is perfectly elastic and the ball rebounds to the same height and again falls Find the average force exerted by the ball on the floor during a long time interval

This section contains 10 questions Three particles are located at the vertices of an equilateral triangle whose sides equal to a 3m They all start moving simultaneously with speed v 2m s with the first particle heading continually for the second the second for the third and the third for the first How soon will the particles meet

4 Answer the following questions in 60 80 words a A train starts from rest and accelerates uniformly for 30 seconds to acquire of 108 km h It travels with this velocity for 20 minutes The driver now appe and the train slows down uniformly to stop after 20 seconds Find the total covered by the train b A velocity time graph of a car is plotted below Observe the graph to following questions velocity m s 8 6 st 2 0 2 1 8 4 6 time seconds 10 2021 6 8 11 48 i Find the acceleration during the first 4 seconds of motion ii Find the average velocity during the first 4 seconds of motion iii Find the average speed of the car over the 10 seconds

III a Find the curve joining two points along which a particle falling from rest under the influence of gravity travels from the higher to the lower point in least time DO

While moving with uniform acceleration a body has covered 100m in 10th second and attained a velocity of 105 m s Its initial velocity u and acceleration a respectively are 2 A 10 ms 5 ms 2 ms 10 ms ex 5 ms 2 B 10 ms 5 ms D 10 ms 0 ms

Two cars A B start moving from same point on a straight road in same direction Car A has constant speed of 20 m s car B has constant acceleration of 10 m s and zero initial speed Which of the following is are correct A Car B will overtake car A at t 2 sec B Car B will overtake car A at t 4 sec C Car B will never overtake car A D Distance travelled by car B at the time of overtaking is 80 m

A particle is projected vertically upward with velocity u from ground when it returns to the point of projection A Its average speed is u 2 C Its displacement is zero B Its average velocity is zero D Its average speed is u

The 1 dimensional motion of a particle is described by the acceleration time graph given below Choose the appropriate qualitative velocity time and position time graphs for this particle Assume the particle starts at x 0 with v 0 A C Straight Line a t Straight Line t B D Straight Line Straight Line

X The equation of trajectory of a projectile is given by y x 3 20 A Minimum speed of the projectile will be 10 m s B Speed of projection will be 20 m s C Time of flight of the projectile will be 3 seconds D Maximum height attained by the projectile will be 15 m Then

Rain droplets are falling in vertically downward direction with velocity 5 m s A cyclist is moving in northward direction with velocity 10 m s The rain droplets will appear to the cyclist to be coming from A tan 2 above south horizon B tan above north horizon C Vertically downward D tan 2 above north horizon

350 m s and there is no wind A material point moving along a straight line enters an 87 5 m segment with speed 5 0 m s and leaves with speed 10 m s The particle crosses the segment with unidirectional acceleration that never exceeds 1 0 m s Find range of average acceleration of the point on this segment Two balls are dropped from the top of a cliff at a time interval At 2 s

A boat is moving with velocity v 2m s w r t river at an angle 0 30 Velocity of river is u 4m s A man at the bank is moving with velocity as shown in figure Boat is moving perpendicularly to the bank w r t the man then v is C D V

6 0 s The maximum possible acceleration of a train moving on straight track is 10 m s and maximum possible retardation is 5 m s Find the minimum time in which the train can complete a journey o 1000m provided The maximum speed that train can achieve is 70 m s ii The maximum speed that train can achieve is 85 m s

A running man has the same kinetic energy as that of a boy of half his mass The man speeds up by 2ms and the boy changes his speed by x ms so that the kinetic energies of the boy and the man are again equal Then x in ms is Question Type Single Correct Type 1 2 2 2 2 2 3 2

7 A horizontal circular disk of uniform thickness radius a and weight I can rotate freely about its vertical geometric axis Fig F Along a circular track of radius r a particle of weight Q is travelling Initially the disk and the particle are rest what angular velocity will the disk acquire if the particle begins to travel along the track with a constant speed v relative to the disk Assume W 10 lb Q 1 lb a 10 in r 6 in v 4 fps Ans 0 537 sec 8 Owing to cooling the linear dimensions of a solid homogeneous sphere uniformly rotating about a diameter diminish by 0 1 per cent What effect will this have on the angular velocity of there is no external moment with respect to the diameter of the sphere Ans The angular velocity increases by 0 2 percent 9 The wheel of a small gyroscope is set spinning by pulling on a string wound around the shaft The moment of inertia of the wheel is 0 045 Ib sec in and the diameter of the shaft on which the string is wound is 1 2 in If 36 in of string is pulled off with a constant force of 12 lb what rpm will be imparted to the wheel An 1 324 rpm at 10 A slender prismatic bar of total length 21 and weight 2W is bent in a right angle its middle point 0 and hangs from a hinge at this point as shown in Fig G Find the maximum angular velocity 8 that the bar will acquire if released from rest in the position shown Ans 0 0 621g l 11 If the slender prismatic bar AB shown in Fig H is released from rest in the horizontal position and rotates about A under the influence of gravity find the reaction at A as it swings through the vertical positions Ans R 5W 2 NG F volls FG G FIG 11 12 A slender prismatic bar DE of length I and weight is rigidly attached at its mid point C to a shaft AB and makers therewith an angle a as shown in Fig L Determine the kinetic energy T of the bar of it rotates with constant angular velocity about AB The following numerical data are given W 20 lb 1 40 in a 45 and the uniform angular speed is 200 rpm Ans T 755 in lb 13 A homogeneous slender prismatic bar AB of length and weight Wis hinged at its lower end 4 and can rotate freely in the vertical plane as shown in Fig If the bar is released from rest in the unstable position and falls over under the influence of gravity calculate the horizontal component of the reaction at A when 30 Ans X 0 225 W K mwin 15 In Fig K a rotor of weight W 386 lb and radius of gyration ie 4 in is mounted on a horizontal shaft and set in rotation by a falling weight W 386 lb as shown If the system is released from rest find the velocity of the block after it has fallen through a distance of 10 ft Ans v 11 35 fps HG 1 14 What initial angular velocity a should be given to the bar AB in Fig J in the top position in order that it will swing through the lowest position B vertically below A with angular velocity 2m Ans 2g l 16 A homogeneous plate 1 ft square is supported in a vertical plane as shown in Fig L a If the pin at 8 is removed what angular velocity u will the plate acquire by the time the diagonal AC becomes vertical b Calculate vertical reaction Re for the instant when the diagonal AC of the square is vertical Ans a e 4 47 rad sec b R 1 44 10 J LA

A stone is dropped from rest off of a bridge It takes 2 seconds for the the stone to hit the water below How high above the water surface is the bridge Use g 10m s 2 a 5 m b 10 m c 20 m d 45 m e 80 m

Three blocks A B and C each of mass m are arranged in pulley string system as shown in the figure All pulleys are massless and frictionless while all strings are light and inextensible Coefficient of kinetic friction u between block A and horizontal surface is equal to 0 5 and force P acts on it The value of P mg for which block C does not move is m m B

One end of uniform wire of length L and of weight W is attached rigidly to a point in the roof and a weight W is suspended from its lower end If s is the area of cross section of the wire the stress in the wire at a height L 4 from its lower end is 1 1 3 W S W 3W 4 2 4 W S W 4 W W

B 1 32 F 2 2 F 3 8 F 4 16 F A block pressed against the vertical wall is in equilibrium The minimum coefficient of friction is mg m mg 2

A body is projected horizontally with a velocity of 10 m s from the top of an inclined plane of angle 45 If it is to hit the foot of the plane and acceleration due to gravity is 10 m s2 the height of the plane in m is

A particle travels half the distance with v For the next one third of total distance it moves such that it travels at v for one third of time and with v for the rest two third of time Now the remaining journey it travels such that it moves with v4 for half the distance and with v for the remaining Find the average speed for the complete journey

The following figure shows the velocity and acceleration of a point like body at the initial moment of its motion The acceleration vector of the body remains constant The time in sec after which its speed becomes 8 m s again is 120 a 2 m s Vo 8 r

A blue ball is thrown upward with an initial speed of 23 3 m s from a height of 0 5 meters above the ground 2 9 seconds after the blue ball is thrown a red ball is thrown down with an initial speed of 8 5 m s from a height of 29 7 meters above the ground The force of gravity due to the earth results in the balls each having a constant downward acceleration of 9 81 m s What is the speed of the blue ball when it reaches its maximum height How long does it take the blue ball to reach its maximum height What is the maximum height the blue ball reaches What is the height of the red ball 3 77 seconds after the blue ball is thrown How long after the blue ball is thrown are the two balls in the air at the same height

c 33 g d 44g b 22g 40 A body is thrown upwards with velocity 40 m and it covers 5 m in the last second of its upd journey If the same body is thrown upwards with velocity 80 ms what distance will it travel in the last second of upward journey Take g 10ms c 15 m d 20 m a 5m b 10 m A machine gun is m a

A projectile is fired at a speed of 100 m s at an angle of 37 above the horizontal At the highest point the projectile breaks into two parts of mass ratio 1 3 the smaller coming to rest Find the distance from the launching point to the point where the heavier piece lands 1 960 m 3 830 m 2 1120 m 4 720 m

Use the worked example above to help you solve this problem A car traveling at a constant speed of 25 3 m s passes a trooper hidden behind a billboard as in the figure One second after the speeding car passes the billboard the trooper sets off in chase with a constant acceleration of 3 59 m s a How long does it take the trooper to overtake the speeding car S b How fast is the trooper going at that time m s

A3m 2m B 2m C Figure 5 Three particles A B and Chave masses 3m 2m and 2m respectively Particle C is attached to particle B Particles A and B are connected by a light inextensible string which passes over a smooth light fixed pulley The system is held at rest with the string taut and the hanging parts of the string vertical as shown in Figure 5 The system is released from rest and A moves upwards a i Show that the acceleration of 4 is 993 ii Find the tension in the string as A ascends At the instant when A is 0 7 m above its original position C separates from B and falls away In the subsequent motion A does not reach the pulley b Find the speed of A at the instant when it is 0 7 m above its original position c Find the acceleration of A at the instant after C separates from B d Find the greatest height reached by A above its original position 2 3

ash 15 m d 20 m 41 A machine gun is mounted on a 2000 kg car on horizontal frictionless surface At some instant the gun fires 10 bullets second each of mass 10 g with velocity of 500 m s The acceleration of the car is 0 25 m s a 0 025 m s c 0 5 ms2 500 m b d Late 2 c 48 A bu Woo in P

Equation of a particle moving along the x axis is x u t 2 a t 2 O the initial velocity of the particle is u O the acceleration of the particle is a O the acceleration of the particle is 2a O at t 2 particle is not at origin

dt A jet of water from a tube of area of cross section A strikes a wall normally with a velocity Vand then flows down along the wall The force exerted on the wall is F AV d If water bounces back with velocity u then F Adv v u If water bounces back with same velocity V then F 2A dv If water strikes at an angle 0 to the surface of wall and reflects then F 2A dv sin 0

c 2 G m m d 2 G m m 6 Two projectiles A and B thrown with speeds in th ratio 1 2 acquired the same heights If A is thrown at an angle of 45 with the horizontal the angle of projection of B will be a 0 b 60 c 30 d 45

3 27 30 A body of mass m thrown horizontally with velocity v from the top of tower of heighth touches the level ground at distance of 250m from the foot of the tower A body of mass 2m thrown horizontally with velocity from the top of tower of height 4 h will 2 touch the level ground at a distance x from the foot of tower The value of x is a 250 m c 125 m b d 500 m 250 2 m

C 3 A boy start towards east with uniform speed 5m s After t 2 second he turns right and travels 40 m with same speed Again he turns right and travels for 8 second with same speed Find out the displacement average speed average velocity and total distance travelled action D Equations of motion and motion under gravity

a mva x Z 5 A particle of mass m is moving in YZ plane with a uniform velocity v with its trajectory running parallel to ve Y axis and intersecting Z axis at z a in figure The bas change in its angular momentum about the origin as it bounces elastically from a wall at y constant is Y b 2 mva x 5 a c ymv X V 002 6 LI NCERT Exempla d 2 ymv x XC 5 with a or x8 1 ir moving

When a parachute opens the air exerts a large drag force on it This upward force is initially greater than the weight of the sky di and thus slows him down Suppose the weight of the sky diver is 969 N and the drag force has a magnitude of 1095 N The masse the sky diver is 98 9 kg Take upward to be the positive direction What is his acceleration including sign Number i Units

d If the surface on which blocks are moving has friction then collision cannot be elastic 21 A block of mass m 2 kg is resting on a rough inclined plane of inclination 30 as shown in figure The coefficient of friction between the block and the plane 0 5 What minimum force F should be applied perpendicular to the plane on the block so that block does not slip on the plane g 10 ms a 2 68 N c 4 34 N 30 b Zero d 6 24 N

Velocity time graph for an object having velocity v 3 t is represented as below velocity 2 3 time Find the distance covered by the object from initial position in 4 s A B 16 m 64 m C 21 3 m 192 m

The distance and displacement for an object moving on the track along the path OAB if it starts and ends at the same point i e the origin as shown in the figure below is given by Given radius r 1m O A B C D 45 B A displacement 2 m distance 2 78 m displacement 0 distance 2 78 m displacement 2 m distance 3 78 m displacement 1 m distance 2 78 m

Figure shows two swimmers starting from point A and Bo instant with a constant velocity Both of them are swimmin AB always The river flows towards east B d River east A A Swimmers A and B cannot collide B Swimmers A and B will definitely collide some where on C Swimmers A and B will definitely collide some where to D Swimmers A and B will definitely collide some where in

An object is suspended from a spring balance in a lift the reading is 240 N when the lift is at rest If the spring balance reading now changes to 220 N then the lift is moving Question Type Single Correct Type 1 downward with constant speed 2 downward with decreasing speed 3 downward with increasing speed

Q 12 A block of weight 100 N is slowly slid up on a smooth incline of inclination 37 by a person Calculate the work done by the person in moving the block through a distance of 2 0 m if the driving force is a parallel to the incline and b in the horizontal direction

What is the relationship between time of flight T and horizontal range R where 8 is angle of projection with the horizontal a R 8T b R 872 2 tan0 c d R tan0 2tan0 7 The disc of a siren revolves 600 times in one minute and it is in unison with a tuning funks tan0 872 R 3