What conclusion can you draw about acceleration?

• Answer:

  Here    u = 0 Using      

  
   
  
  
                   

  Time (in seconds)	Distance (in metres)	A = 2s/t2
  0	0	0
  1	1	2
  2	8	4
  3	27	6
  4	64	8
  5	125	10
  6	216	12
  7	343	14

    Thus acceleration is increasing. (b) As F = ma, therefore,
  
   Hence, the force must also be increasing uniformly with time.
  

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Page 2

• Answer:

  Here, mass of motorcar, m = 1200 kg Let each person exert a push F on the motorcar. Total push of two persons = F + F = 2 F                                                  As this push gives a uniform velocity to the motocar along a level road, it must be a measure of the force of friction (f) between the motorcar and the road, i.e., f = 2F When three person push, total force applied F + F + F = 3F                            Force that produces acceleration (a = 0.2 m s-2), i.e., Ma = 3 F – f = 3 F - 2 F = F or F = ma = 1200 x 0.2 = 240 N
  

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Page 3

• Answer:

  The force of nail on the hammer,                                             

  
   
  
  
  
  Minus sign denotes the force of nail on the hammer, is acting in the direction, opposite to that of hammer.
  

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Page 4

• Answer:

  Here, mass, m = 1200 kg Initial velocity,

  
  
  Final velocity,
  
  
  Time,
  
  Acceleration,
  
  
  (ii) Change in momentum
  
  
  Magnitude of change in momentum = 24000 kg
  
  (iii) Force, F = ma = 1200(-5) = - 6000 N
  
   Magnitude of force = 6000 N.
  

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Page 5

Answer:

Let mass of truck = M Velocity of car

time for which collision lasts,

(a) On collision, both the vehicles experience the same force, as action and reaction are equal. (b) Change in momentum of truck is equal and opposite to change in momentum of car, i.e., both the vehicles experience the same change in momentum. (c) As acceleration = force/mass, and force on each vehicle is same, acceleration

As mass of car   is smaller, therefore, acceleration of car is greater than the acceleration of the truck. (d) The car is likely to suffer more damage than the truck, as it is lighter. The acceleration, i.e., change in velocity of car is more than that of the truck.

Page 6

• Answer:

  (c) For an object moving along a straight path in an accelerated motion, it is not necessary that it always goes away from the earth.
  

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Page 7

• Answer:

    (b) According to third law of motion, action and reaction always act on different bodies in opposite directions.
  

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Page 8

• Answer:

    (d) The goalkeeper pulls his hands backwards after holding the ball to decrease the rate of change of momentum by increasing the time. By doing this, less force is exerted on his hands (

  
  Force is directly proportional to the rate of change of momentum).
  

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Page 9

• Answer:

    (c) The inertia of an object tends to cause the object to resist any change in its state of rest or motion.
  

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Page 10

• Answer:

    (a) If the coin falls behind the passenger that means the train is accelerated. When the coin is tossed it has same velocity as that of train but during the time it is in air its velocity becomes less than that of train (because the train is accelerated), so it falls behind the passenger.
  

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Page 11

• Answer:

    (b) Given, mass m = 2 kg, velocity

  
  As the object is moving with a constant velocity i.e.,
  
  so the acceleration of the object is zero i.e., a = 0 and according to the property of inertia if there is no external force acting on the body, then body remains as it is i.e., if the body is at rest, remains and if it is in motion remains in motion.
  

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Page 12

• Answer:

    (c) Rocket works on the conservation of momentum. In a rocket, the fuel burns and produces gas at high temperature. These gases are ejected out of the rocket from a nozzle at the back side of the rocket. The ejecting gas exerts a forward force on the rocket which help in accelerating. Through the mass of gases escaping per second is very small and their momentum is very large due to their tremendous velocity of escape. An equal and opposite momentum is imparted to the rocket which despite its large mass builds up a high velocity.
  

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Page 13

• Answer:

    (b) On the sudden application of brake, the tanker will come in the state of rest but the water remains in the state of motion, so the water will move forward.
  

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Page 14

• Answer:

    As the mass is a measure of inertia the ball of same shape and size having more mass than other balls will have highest inertia. Since, the steel has greatest density and greatest mass therefore it has highest inertia.                              
  

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Page 15

• Answer:

    When the train is stopped suddenly, then it comes in the state of rest but the balls remain in the state of motion. So, due to inertia of motion, the balls move in the forward direction. As the balls are of same size but of different materials that means their mass will be different. So, both the balls will move with different speeds.
  

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Page 16

• Answer:

    As both the bullets are identical and are fired with the same force. So, to reduce recall velocity, we use, heavy rifle so that its heavy mass compensate the large momentum. But for light rifle, recoil velocity will be large due to small mass thus light rifle will hurt more to the shoulder.
  

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Page 17

• Answer:

        When the cart starts moving, frictional force starts working on the wheel of cart in opposite to the motion. So, horse need to apply continuous force in forward direction to maintain constant speed.
  

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Page 18

• Answer:

    Momentum of a system remains conserved if no external force acts on the system. In the given example, there is gravitational force acting on the ball which is an external force, so it is not an example of conservation of momentum.
  

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Page 19

• Answer:

    Given, mass,

  
                    
  
  Initial velocity,
  
  Final velocity,
  
  Time taken,
  
  From first equation of motion v = u + at
  
  
   Acceleration,
  
    [Negative sign shows retardation] Now, frictional force of the floor on the ball
  
   [Negative sign showns against the direction of motion]
  

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Page 20

• Answer:

    Let, initial mass,

  
   Initial force,
  
  According to the question, new mass,
  
  and new force,
  
      From Newton's second law, F = ma
  
   
  
  Change in acceleration
  
  
           
  
  
           
  
  Hence, the new acceleration will be one-fourth of previous acceleration.
  

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Page 21

• Answer:

    Separation between them will increase. Initially the momentum of both of them are zero as they are at rest. In order to conserve the momentum the one who throws the ball would move backward.                                                 The second will experience a net force after catching the ball and therefore will move backward that is in the direction of the force.
  

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Page 22

• Answer:

    Water sprinkler works on Newton's third law of motion. When the water supplied, then force applies on the sprinkler due to which it rotates.
  

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Page 23

Answer:

  If a body of mass (m), moving at velocity (u) accelerates uniformly at.(a) for time 'f, so that its velocity changes to v, then initial momentum

and final momentum

Change in momentum

According to the second law of motion, force

               

                         

                         

               [where,

] Here,                        

                          

Given,  

and

(i) From third equation of motion,       

                         

                         

Now, force applied, by the bullet,  F = ma

[negative sign shown against the direction of motion] The resistive force exerted by the sand on the bullet = 105 N (i)From first equation of motion, v = u + at

                          at = v - u Now, time taken by bullet to come to rest.

  

                         

                         

                         

Hence, force (F) = 105 N and time   

Page 24

Answer:

  We know that, Sl unit of mass, m=1kg Sl unit of acceleration, a = 1

Now, from Newton's second law, F = ma

Sl unit of force, F = 1 kg x 1

  = 1 kg-

kg-

 is known as

1 newton (N) newton (N) = 1 kg-

1 newton can be defined as, "the force is said to be 1 newton if it produces 1

 acceleration in a body of 1 kg mass". Condition I Given,

and

 mass of first body

 and

 mass of second body From Newton's second law, F = ma or 5 = m, x 8

                                         

Condition II Again, using Newton's II law

                                         

Sum of two masses

Acceleration produced by the same force provided if both the masses are tied together. i.e.,

                                  F = same

              

combined mass                

               

Hence, the acceleration is

.

Page 25

• Answer:

    Momentum The quantity of motion possessed by a moving body is known as momentum of the body. Momentum of an object of mass m moving with a velocity v is the product of it. It is denoted by p p= mv Its Sl unit is

  
  . As from Newton's lInd law, rate of change of momentum is equal to force applied. So,
  
                                  
  
  
  
   Hence, force applied on an produces acceleration,           (i)Momentum versus velocity when mass is fixed,                          
  
  If m is fixed, then            
  
  
  
  Momentum versus velocity graph will be a straight line passing through the origin (if v = 0, then p = 0).         (ii) Momentum versus mass graph when velocity is constant for different body                                
  
  
  If velocity is constant for different masses, then        
  
  So, the momentum versus mass graph will be a straight line passing through the origin (if m = 0, then p= 0).           
  

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