FORCE AND MOTION Tick ( ) the most appropriate answer.

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1 2 FORCE AND MOTION I. Tick ( ) the most appropriate answer. 1. A book lying on a table is an xample of (a) a body in motion (b) a body at rest (c) a body neither at rest nor in motion (d) none of these 2. A car moving on a straight road is an example of (a) oscillatory motion (b) rotatory motion (c) rectilinear motion (d) periodic motion 3. The kind of motion that a pendulum has is (a) curvilinear (b) rotatory (c) oscillatory (d) rectilinear 4. An example of curvilinear motion is (a) an apple falling from a tree (b) a spinning wheel (c) the motion of a pendulum (d) throwing of a javelin 5. A person driving a car is in a state of rest with respect to (a) a post box on the roadside (b) a hospital (c) the roof of the car (d) a hoarding on the road 6. The time taken by the bob of a pendulum to complete one oscillation is called its (a) amplitude (b) time period (c) frequency (d) oscillation 7. Distance is a (a) scalar quantity (b) vector quantity (c) normal quantity (d) none of these 8. The quantity which tells the distance of an object travels in a certain time is called (a) acceleration (b) speed (c) velocity (d) none of these 9. It two bodies are moving with the same speed but in different directions, they will have (a) same velocities (b) same acceleration 1

2 (c) different velocities (d) none of these 10. A body moving with a constant velocity will have (a) constant acceleration (b) constant retardation (c) zero acceleration (d) none of these 11. A wooden bench lying in the corner of a garden is an example of (a) body in motion (b) body in rest (c) body neither in state of rest nor motion (d) none of these 12. A body moving at a uniform velocity of 2 ms 1 will have (a) uniform acceleration (b) non-uniform acceleration (c) zero acceleration (d) none of these 13. The unit of frequency of pendulum is (a) metre (b) second (c) hertz (d) none of these 14. The time taken by a freely suspended pendulum to complete one oscillation is (a) amplitude (b) frequency (c) time period (d) none of these 15. A person sitting in a speeding train is at rest with respect to (a) trees (b) fields (c) buildings (d) other passengers 16. The rate of change of velocity is known as (a) speed (b) displacement (c) acceleration (d) none of these 17. When a drill bores a hole in a piece of wood, it describes (a) rotatory motion (b) translatory motion (c) curvilinear motion (d) rotatory and translatory motion 18 A freely falling stone has (a) uniform speed (b) uniform velocity (c) uniform acceleration (d) uniform motion 19. The motion described by the string of violin is (a) oscillatory motion (b) vibratory motion 2

3 (c) non-periodic motion (d) rectilinear motion 20. With the increase in length of a simple pendulum, its time period (a) increases (b) decreases (c) remains same (d) none of these Ans. 1. (b) 2. (c) 3. (c) 4. (d) 5. (c) 6. (b) 7. (a) 8. (b) 9. (a) 10. (c) 11. (b) 12. (c) 13. (c) 14. (c) 15. (d) 16. (c) 17. (d) 18. (c) 19. (b) 20. (a) II (A). Fill in the blanks. 1. A tree in a park is in state of. 2. The earth is in state of. 3. A spinning top has a motion. 4. Motion of the earth around the sun is. 5. The frequency of a second s pendulum is. 6. The of a simple pendulum is directly proportional to the square root of its length. 7. The maximum displacement of the bob from its mean position is called its. 8. The travelled by a moving body is the actual lenght of the path covered by it. 9. When a satellite completes one revolution, the displacement of the satellite is. 10. The SI unit of speed is. Ans. 1. rest 2. motion 3. rotatory 4. periodic Hz 6. time period 7. amplitude 8. distance 9. zero 10. metre per second II (B). Fill in the blank spaces by choosing correct words from the list given below. List : increases, speed, rectilinear, gravity, curvilinear, acceleration, rotation, velocity, translation, periodic, oscillatory. 1. A moving carrom board coin describes a motion of. 3

4 2. A ball thrown upwards at an angle describes moton. 3. A wheel of a moving bicycle describes a motion of and motion of. 4. The motion described by a simple pendulum is motion. 5. A motion which repeats itself after a fixed interval of time is called motion. 6. The rate of change of motion is called. 7. The rate of change of motion in a specified direction is called. 8. The rate of change of velocity is called. 9. The acceleration due to 9.8 ms The time period of a simple pendulum with the increase in the length of pendulum. Ans. 1. rectilinear 2. curvilinear 3. translation, rotation 4. oscillatory 5. periodic 6. speed 7. velocity 8. acceleration 9. gravity 10. increases III (A). The statements given below are incorrect. Write correct statement. 1. A ball thrown by a boy from a roof-top has oscillatory motion. Ans. A ball thrown by a boy from a roof-top has rectilinear motion. 2. A motion which repeats itself after a fixed interval of time is called vibratory motion. Ans. A motion which repeats itself after a fixed interval of time is called periodic motion. 3. The length of a second s pendulum at a place, where g = 9.8 ms 2, is 90.2 cm. Ans. The length of a second s pendulum at a place, where g = 9.8 ms 2, is 99.2 cm. 4. If the value of g decreases, the time period of the simple pendulum decreases. Ans. If the value of g decreases, the time period of the simple pendulum 4

5 increases. 5. The unit of frequency is decibel. Ans. The unit of frequency is hertz. 6. Displacement is a scalar quantity. Ans. Displacement is a vector quantity. 7. Velocity is the distance travelled by a moving body per unit time. Ans. Speed is the distance travelled by a moving body per unit time. 8. The SI unit of acceleration is m/s. Ans. The SI unit of acceleration is m/s A body can change its state of rest or of uniform motion on its own. Ans. A body cannot change its state of rest or of uniform motion on its own. 10. With the decrease in length of a simple pendulum, its time period increases. Ans. With the increase in length of a simple pendulum, its time period increases. 11. The motion described by the needle of a sewing machine is a vibratory motion. Ans. The motion described by the needle of a sewing machine is oscillatory motion. 12. The motion of a bus going around a traffic roundabout is a rotatory motion. Ans. The motion of a bus going around a traffic roundabout is a curvilinear motion. 13. The time period of a second s pendulum is 1 second. Ans. The time period of a second s pendulum is 2 second. 14. A runner, running along a circular track at a constant speed has a uniform velocity. Ans. A runner, running along a circular track at a constant speed has a non-uniform velocity. 15. The beating of heart of a healthy person at rest, is a non-periodic motion. Ans. The beating of heart of a healthy person at rest, is a periodic motion. 5

6 16. The moon waxes and wanes while going around the earth, and hence, it has circular motion. Ans. The moon waxes and wanes while going around the earth, and hence, it has periodic motion. 17. The motion described by the string of a violin is oscillatory motion. Ans. The motion described by the string of a violin is vibratory motion. III (B). Write true or false for each statment given below. 1. The motion of a giant wheel is a circular motion. 2. The motion of the moon around the earth is a curvilinear motion. 3. The average acceleration due to gravity is 8.9 ms The units of speed and velocity are same in SI system. 5. The rate of change of velocity is called speed. 6. The motion described by wire of sitar is a vibratory motion. 7. The time period of a pendulum increases with the decreases in length. 8. A second s pendulum can be used as a timing device. Ans. 1. True 2. False 3. False 4. True 5. False 6. True 7. False 8. False IV. Find the odd-one out. Give reasons for your choice. 1. Tree, hut, earth, dustbin, chair Ans. Earth because it is in the state of motion while others are in the state of rest. 2. Length of the pendulum, acceleration due to gravity, mass of the bob Ans. Mass of the bob because the time period of a pendulum does not depend on the mass of the bob. 3. Apple falling from a tree, car moving on a straight road, coins moving over a carrom board, giant wheel Ans. Giant wheel because it is the example of rotatory motion while others are examples of rectilinear motion. 4. Displacement, veleocity, acceleration, weight, speed Ans. Speed because it is the scalar quantity while others are vector quantities. 6

7 5. Aeroplane, bird, lion, fish, submarine Ans. Lion because its movement is neither in air nor in water. 6. Length, time period, frequency, acceleration Ans. Frequency because the term is not used to find the time period of a freely oscillating pendulum. 7. Speeding train on a straight railway line, a freely falling stone, coins moving over carrom board, a girl on a swing Ans. A girl on a swing because it is an example of a periodic motion while others are examples of rectilinear motion. 8. Velocity, speed, acceleration, mass Ans. Mass because other terms are related to the motion. V. Give reasons for the following. 1. Rotation of the earth is a periodic motion. Ans. A motion which repeats itself at regular intervals of time is called periodic motion since the earth rotates about its axis and always takes same time that is 24 hours to complete one round hence rotation of the earth is a periodic motion. 2. A boy riding on a moving bicycle has a multiple motion. Ans. A boy riding on a moving bicycle has a multiple motion because the wheels of the bicycle rotates to cause rotatory motion and at the same time the bicycle moves forward in a straight line or curved path to cause translatory motion. VI. Match the following. Physical Quantity SI Unit 1. displacement (a) second 2. velocity (b) metre per second square 3. time (c) metre per second 4. acceleration (d) metre Ans. 1. (d), 2. (c), 3. (a), 4. (b) VII. Differntiate between the following. 1. Rectilinear motion and curvilinear motion Ans. Translatory motion along a stright line is called rectilinear motion 7

8 while translatory motion along a curved line is called curvilinear motion. 2. Vibratory motion and periodic motion Ans. The motion in which a certain part or parts of a body always remain fixed and do not move while the rest of the body moves to-and-fro in a definite style is called vibratory motion. A motion which repeats itself at regular intervals of time is called periodic motion. 3. Scalar quantity and vector quantity Ans. A physical quantity which is described completely by its magnitude is called a scalar quantity. A physical quantity which is described completely by its magnitude as well as direction is called a vector quantity. 4. Distance and displacement Ans. The actual length of a path covered by a moving body, irrespective of its direction, is called the distance travelled by the body. It is a scalar quantity. The shortest distance covered by a moving body in between two points in a particular direction is called its displacement. It is a vector quantity. 5. Speed and velocity Ans. The distance travelled by a moving body per unit time is called its speed. It is a scalar quantity. The distance travelled by a body per unit time in a given direction is called its velocity. It is a vector quantity. VIII. Define the following terms and also give one example of each. 1. Random motion Ans. Random motion: A body which has a particular motion that suddenly changes to another kind of motion is said to have random motion. For example, when a mosquito is in flight, at one moment it may have translatory motion, at the next moment it may have rotatory motion. Such a motion is called random motion. 2. Multiple motion 8

9 Ans. Multiple motion: Sometimes an object possesses two or more types of motion at the same time. Such motion is called multiple motion. For example, when a spin bowler delivers a ball the ball has a motion of spin (rotatory motion) while it moves towards the batsman (translatory motion). 3. Second s pendulum Ans. Second s pendulum: A pendulum which completes its one oscillation in two seconds is known as a second s pendulum. The length of a second s pendulum at a place where g = 9.8 m/s 2 is 99.2 cm. A second s pendulum is independent of amplitude. Its frequency 9 n = 1 2 Hz IX. Answer these questions. 1. What is oscillatory motion? Give two examples. Ans. A motion in which the body as a whole moves to-and-fro about its mean position is called oscillatory motion. Examples The motion of a swing. The motion of pendulum of a clock. 2. What is translatory motion? Name two kinds of translatory motion. Ans. If an object moves in a line in such a way that every point on the object moves through the same distance in the same interval of time the motion of the object is called translatory motion. Examples A ball rolling on the ground. A stone falling freely from the roof of a building. 3. Give an example to show that rest and motion are relative terms. Ans. Imagine you are travelling by a train. You are in motion in relation to a farmer standing in a field or trees on the platform because your position is changing with respect to them. However, if you compare your position with respect to the things inside the train, that is other passangers, walls, fans, etc. it is not changing. Therefore, in relation to these objects you are at rest, thus, an object can be in motion in relation to one set of objects while it is at rest in relation to another set of objects. We can say that rest and motion are relative terms. It

10 is the observer and the surroundings that decide whether a given object is considered at rest or in motion. 4. What is a simple pendulum? What are the factors affecting the time period of a simple pendulum? Ans. Simple pendulum. A simple pendulum consists of a small metal ball (called bob) suspended by a long thread from a rigid support. Such that the bob is free to swing back and forth. The time period of a simple pendulum depends upon the following factors. 1. Length. The time period of a simple pendulum is directly proportional to the square root of its length T 2. Aceleration due to gravity. The time period of a simple pendulum is inversely proportional to the square root of the acceleration due to gravity at that place 1 T g 3. Mass of the bob. The time period of a simple pendulum is independent of the mass of the bob, that is, if we use bobs of different masses its time period does not change. 4. Nature of the material of the bob. The time period of a simple pendulum is independent of the nature of the material of the bob. 5. Classify the following into translatory, rotatory and oscillatory motions. (a) ball thrown by a child (b) giant wheel (c) piston of a car (d) swinging pendulum (e) freely falling stone (f) spinning top (g) charkha (h) throwing of a javelin (i) potter s wheel Ans. (a) Ball thrown by a child Translatory motion (b) Giant wheel Rotatory motion (c) Piston of a car Oscillatory motion (d) Swinging pendulum Oscillatory motion 10 l

11 (e) Freely falling stone Translatory motion (f) Spinning top Rotatory motion (g) Charkha Rotatory motion (h) throwing of a javelin Translatory motion (i) Potter s wheel Rotatory motion 6. By giving at least two examples each, define the following terms. (a) Rectilinear motion (b) Curvilinear motion (c) Rotatory motion (d) Oscillatory motion (e) Vibratory motion (f) Periodic motion Ans. (a) Rectilinear motion. When an object moves along a straight line, its motion is called rectilinear motion. Examples A ball rolling on the ground A car moving on a straight road. (b) Curvilinear motion. If an object moves along a curved path its motion is called curvilinear motion. Examples A stone thrown by a boy A car moving along a curved path (c) Rotatory motion. A body is said to be in rotatory motion if it moves about a fixed axis without chaning its position. Examples The motion of the blades of a fan A giant wheel (d) Oscillatory motion. A motion in which the body as a whole moves to-and-fro about its mean position is called oscilltory motion. Examples The motion of a swing The pendulum of a clock (e) Vibratory motion. The motion in which a certain part or parts of a body always remain fixed and do not move, while rest of the body moves to-and-fro in a definite style is called vibratory motion. Examples A string of a guitar or a sitar when plucked starts vibrating. During breathing, our chest expands and contracts this motion is vibratory in nature. (f) Periodic motion. A motion which repeats itself at regular intervals 11

12 of time is called periodic motion. Examples The motion of the earth around the sun The needle of a sewing machine 7. Define : (i) rest, (ii) motion. Ans. (i) Rest A body is said to be at rest, if it does not change its position with respect to a fixed point in its surroundings. For example a book lying on a table. (ii) Motion A body is said to be in motion, if it changes its position with respect to a fixed point in its surroundings. For examples, a man walking on the road. 8. Define : (a) speed, (b) velocity. Bring out clearly the difference between speed and velocity. Ans. (a) Speed The distance travelled by a moving body per unit time is called its speed. (b) Velocity The distance travelled by a body per unit time in a given direction is called its velocity. Speed is a scalar quantity whereas velocity is a vector quantity. 9. (a) Define : (i) acceleration, (ii) acceleration due to gravity. Ans. (i) Acceleration The rate of change of velocity of a body is called its accleration. change in velocity acceleration = time taken The SI unit of acceleration is meter per second square (m/s 2 ) (ii) Acceleration due to gravity The acceleration with which a body falls freely towards the earth is called acceleration due to gravity. It is denoted by the symbol g. The numerical value of acceleration due to gravity is 9.8 m/s 2. This value changes from place to place and at the same place it changes with altitude. 10. What do you understand by the terms (a) uniform velocity, (b) variable velocity? Give one example of each. Ans. (a) Uniform velocity When a body covers equal distances in equal interval of time in a specified direction the body is said to be 12

13 moving with a uniform velocity. Example Imagine a car is moving along a straight road towards east, such that in every one second it covers a distance of 5 m. In such a case, the uniform velocity of car is 5 m/s east. (b) Variable velocity When a body covers unequal distances in equal intervals of time in a specified direction or equal distances in equal intervals of time, but its direction changes, then the body is said to be moving with a variable velocity. Example Consider a body starting from point A and reaches B, C and D straight towards east in the time intervals of 1 second each. Let the distances covered be 3m, 4m and 2m respectively. As the body is covering unequal distances in equal intervals of time in a specified direction, therefore, the body is moving with variable velocity. 11. Prove : v = u + at, where u is the initial velocity, v is the final velocity, a is the acceleration and t is the time. Ans. Let us consider a body having an initial velocity u. After time t, the body moves with a velocity v. From the definition of acceleration, we get change in velocity Acceeleration = time taken final velocity initial velocity = time taken v u a = t at = v u or, v = u + at 12. Define the following with reference to simple pendulum: 13

14 (a) pendulum (b) mean position (c) oscillation (d) time period (e) amplitude Ans. (a) Pendulum A small metallic bob (brass or any other material) tied to a light, cotton thread and suspended from a rigid point, such that it is free to oscillate about its mean position is called a pendulum or simple pendulum. (b) Mean position When a freely suspended pendulum is at rest then this position is called mean position or rest position. (c) Oscillation The complete to and fro motion of a freely oscillating pendulum about its mean position is called oscillation. (d) Time period The time taken by a freely oscillating pendulum to complete one oscillation is called time period. Its SI unit is second. (e) Amplitude The maximum displacement of a pendulum from its mean position is called amplitude. 13. What is a second s pendulum? What is the length of second s pendulum. Ans. A simple pendulum whose time period is 2 second is called second s pendulum. The length of a second s pendulum at a place where g = 9.8 m/s 2 is 99.2 cm. A second s pendulum is independent of amplitude. Its frequency n = ½ Hz 14. The length of second s pendulum is shortened by 20 cm. How this change in length will affect the time period of the pendulum? Ans. The time period of a freely oscillating pendulum is given by the expression T = 2 l g Where T is the time period in seconds, l the length of the pendulum and g the acceleration due to gravity at a given place. From the above expression it is clear that T l i.e. as the length of a pendulum increases, so will increase its time period and vice versa. Therefore, if the length of second s pendulum is shortened by 20 14

15 cm its time period will also shortened. 15. What is meant by the term retardation? Name its SI unit. Ans. If the velocity of a body is decreasing with respect to time, the acceleration is said to be negative. This negative acceleration is called retardation. The SI unit of retardation is meter/second 2 (m/s 2 ). X. Practice for numerical problems. 1. Calculate the speed of a car moving a distance of 150 km in 3 hours. Ans. Distance (D) = 150 km Time (t) = 3 hours Speed (S) = Distance (D) Time (t) 150 km = = 50 km/h 3 hours 2. Calculate the time taken by a train moving at a speed of 50 km/h if it covers 250 kilometres. Ans. Speed (S) = 50 km/h Distance (D) = 250 km Time (t) = Distance (D) 250 km = Speed (S) 50 km/h = 5 h 3. Calculate the distance travelled by a bicycle moving at a speed of 20 km/h in 2 hours. Ans. Speed (S) = 20 km/h Time (t) = 2 hours Distance = speed (S) time (t) = 20 km / h 2 h = 40 km 4. A car starting from rest, picks up a velocity of 15 m/s in 20 seconds. Find the acceleration of the car. Ans. Initial velocity (u) = 0 Final velocity (v) = 15 m/s Time (t) = 20 s Acceleration (a) = v u 15 0 = m/s 15 t 20

16 = m/s2 = 0.75 m/s 2 5. A car is travelling at 15 m/s. If its velocity increases to 20 m/s in 5 s then find the acceleration of the car. Ans. Initial velocity (u) = 15 m/s Final velocity (v) = 20 m/s Time (t) = 5 s Acceleration (a) = v u = m/s t 5 2 = 1 m/s 2 6. A scooter is travelling with a certain speed. Its final velocity becomes 30 m/s in 5 s accelerating at the rate of 2 m/s 2. Find its initial velocity. Ans. Let the initial velocity = u Final velocity (v) = 30 m/s Time (t) = 5 s Acceleration (a) = 2 m/s 2 Acceleration (a) = v u t 2 = 30 u 5 or, 10 = 30 u or, u = 20 m/s 7. A car is travelling at 20 m/s. If its velocity increases to 30 m/s while accelerating at the rate of 5 m/s 2, find the time taken to accelerate. Ans. Let the time taken be t seconds Initial velocity (u) = 20 m/s Final velocity (v) = 30 m/s Acceleration (a) = 5 m/s 2 5 Time (t) =? Acceleration (a) = v u t 16

17 5 = t or, t = 10 = 2 seconds 5 8. A scooter is travelling at 10 m/s. Find its velocity if the scooter is accelerating at the rate of 2 m/s 2 in 7 s. Ans. Let the final velocity be v m/s Initial velocity (u) = 10 m/s Acceleration (a) = 2 m/s 2 Time (t) = 7 s Acceleration (a) = v u t 2 = v 10 7 or, 14 = v 10 or, v = 24 m/s 9. Draw a velocity-time graph of a moving car from the data given in the following table. Also indicate the acceleration in the graph. velocity (m/s) time (s) Ans. The slope of the graph AC gives the acceleration of the body. 17

18 10. A horse runs a distance of 1200 metres in 3 min and 20 seconds, what is the speed of the horse. Ans. Distance (D) = 1200 metres Time (t) = 3 min 20 seconds = 200 seconds Distance (D) 1200 metres Speed (S) = = Time (t) 200 seconds = 6 m/s 11. A bus is moving at 20 metre/sec. How much distance in kilometre will the bus cover in 25 minutes? Ans. Let the distance be D km Speed (S) = 20 m/s = km/h 1000 = 72 km/h Time (T) = 25 min = h Distance (D) = Speed (s) Time (t) = 72 km/h h = 30 km 12. A motor bike is moving with a velocity of 5 metre/second. Its velocity increases to 25 metre/second over a time span of 10 second. Calculate the acceleration produced by the motor bike. Ans. Initial velocity (u) = 5 m/s Final velocity (v) = 25 m/s Time (t) = 10 seconds Acceleration (a) = v u t 25 5 = m/s 10 2 = 2 m/s 2 18

19 13. A car starts from rest, if the engine of the car produces an acceleration of 1.5 metre/second 2 for 30 seconds. Calculate final velocity of the car. Ans. Let the final velocity be v m/s Initial velocity (u) = 0 Acceleration (a) = 1.5 m/s 2 Time (t) = 30 seconds Acceleration (a) = v u t 1.5 = v 0 30 or, v = m/s = 45 m/s 14. The velocity of a body changes from 2 metre/second to 20 metre/ second when the acceleration is 2 metre/sec 2. Calculate for how long the acceleration acts. Ans. Let the acceleration last for t seconds Initial velocity (u) = 2 m/s Final velocity (v) = 20 m/s Acceleration (a) = 2 m/s 2 Acceleration (a) = v u t = t or, 2 = 18 t or, t = 18 2 seconds or, t = 9 seconds 15. A body initially having a velocity u is acted upon by an acceleration of 0.5 m/s 2 for 20 s, such that the final velocity of the body is 20 19

20 metre/second. Calculate the velocity u. Ans. Initial velocity (u) = u Final velocity (v) = 20 m/s Acceleration (a) = 0.5 m/s 2 Time (t) = 20 seconds Acceleration (a) = v u t 0.5 = 20 u 20 or, 10 = 20 u or, u = 10 m/s 16. A stone dropped from the top of a building reaches the ground with a velocity of 49 m/s. If acceleration due to gravity is 9.8 m/s 2. Calculate the time for which stone is falling freely. Ans. Let the stone is falling freely for t seconds. Initial velocity (u) = 0 Final velocity (v) = 49 m/s Acceleration due to gravity (g) = 9.8 m/s 2 Using v = u + gt 49 = t t = seconds = 5 seconds 17. A stone dropped from a cliff reaches the ground in 1.5 s. If acceleration due to gravity is 9.8 m/s 2. What is the velocity of stone before hitting the ground. Ans. Let the velocity of stone before hitting the ground be v m/s Initial velocity (u) = 0 Time (t) = 1.5 seconds 20

21 Acceleration due to gravity (g) = 9.8 m/s 2 Using v = u + gt v = or, v = 14.7 m/s 18. A body when projected up goes to a height h in time t and then returns back at the point of projection. Which of the following statement is true: (a) the displacement is zero, (b) the average velocity is 2 h/t, (c) the final speed is double the initial speed, (d) the acceleration is zero. Ans. Since the body returns back to its original position therefore the displacement of the body is zero. 19. The value of g remains same at all places on the earth surface. Is this statement true? Ans. The given statement is not true because the value of g is maximum at poles and minimum at equator. 20. If a stone and a feather are dropped simultaneously in vacuum from the top of a tower, which of the two will reach the ground first. Ans. Both will reach the ground simultaneously since, acceleration due to gravity (g = 9.8 m/s 2 ) is same for both a stone and a feather. 21