## FRICTION

If the switch off the engine of car it will stop after moving a certain distance. It means that some retarding force is acting on the car which stops it. The force opposing the motion of the car is called "force of friction".
(i)    The frictional force is tangential to the surface in contact and always in a direction opposite to the direction of motion of the object.

(ii)    Frictional force is a force opposing the relative motion between two surfaces which are in contact with each other.
(iii)    The force of friction arises due to the interlocking of irregular projections on the two surfaces and is called as "force of contact".

TYPES OF FRICTION
(A)    Static friction :
The frictional force that exists between the body and the surface so long as they are relatively at rest even when the external force acts, is called the static friction.

(B)    Limiting friction :
(i)        When there is no external force acting on the body, the frictional force is zero.
(ii)        If we increase the magnitude of the external force, the static friction also increases.
(iii)        At one pt, when there is a slight increase in the magnitude of the external force, the body just starts sliding over the surface.
(iv)     The force of friction at the limiting stage is called the 'limiting friction.'
(v)         The limiting friction depends upon the nature of the two surfaces in contact.

(C)    Kinetic or Sliding friction :
(i)         When the external force exceeds the limiting friction, the body just starts sliding.
(ii)         The minimum force required to maintain the motion of the body over the other surface is called the "kinetic friction".
(iii)         The frictional force that exists between the two surfaces when there is a uniform relative motion between them is called the "dynamic friction" or "sliding friction".
(iv)     Kinetic friction is smaller than the limiting friction.

(D)    Rolling friction :
(i)     The frictional force that exists between the two surfaces when a body rolls over the other is called the "rolling friction".
(ii)     It deforms the surface over which it rolls.
(iii)     Rolling body it-self gets deformed at the pt of contact over the surface.

*    Variation of frictional force with applied forces :
(i)     The part OA of the graph shows that the static friction increases with the increase in applied force.

(ii)     The force of friction is maximum at a pt A which is equal to AP.
(iii)     If the applied force is increased further, the body will continue to be in motion but the force of friction is slightly lesser.
(iv)     After this the force of friction remains constant.
Note : Rolling friction is smaller than sliding friction which in turn is smaller than the limiting friction.

*  FACTORS AFFECTING FRICTION
The force of friction depends upon the following factors :
(i)     Materials of the bodies in contact.
(ii)     Roughness of the surfaces in contact
(iii)     Force of friction is independent of the area of the two surfaces in contact.
(iv)     The limiting frictional force is directly proportional to the normal reaction.

*  COEFFICIENT OF FRICTION

REDUCING FRICTION

Frictional force can be reduced in the following ways:
1.    Use of lubricants : In

...
friction can be reduced by applying lubricants between the contact surfaces to fill the fine pores or depressions in the surfaces and make them smooth thereby reducing friction.

2.    Polishing : unevenness of the surfaces can be reduced by polishing, thereby reducing the friction.

3.    Use of ball bearings : In rotating machines, shafts are mounted on ball bearings. By doing so, rolling friction occurs lesser than sliding friction, thereby reducing the friction.

4.    By streamlining : Air friction is reduced by designing streamlined bodies of cars or aeroplanes. Similarly, if the bodies of boats and ships are streamlined, friction of water can be reduced.

5.    Wheels:  If a suitcase is fitted with wheels,it is easier to move it because the friction between the wheels and the ground is less.

1.    Wear and Tear : In machine parts like gears, brakes when they come in contact with each
other continuously, they wear out gradually, which should be replaced time to time.
2.    Friction reduces efficiency of the machine.
3.    Friction in machine produces heat and undesirable noise which damages the machine. To avoid excessive heating, water is circulated in machines generally.

APPLICATIONS OF FRICTIONAL FORCES

1.    We would not be able to walk if there had been no friction b/w the soles of our shoes and the ground.

2.    If there had been no friction, the wheels of a car will slip instead of rotating and stop moving. For that we have to increase the friction by making the tyres corrugated to get better grip of tyres on the road. Also, the friction is increased.
3.    When brakes are applied, the vehicle stops due to the force of friction b/w the brake lining and the drum.
4.    In the absence of friction, we cannot write on a blackboard with a chalk stick because the chalk stick will slide off the board without leaving any mark on the board.

SOLVED EXAMPLES

Ex.2    The correct relation between magnitude of f1 and f2 in above problem is :
(A) f1 > f2    (B) f2 > f1    (C) f1 = f2
(D) not possible to decide due to insufficient data.
Sol.    By Newton’s third law the above friction forces are action-reaction pair and equal but opposite to each other in direction. Hence (C)
Also note that the direction of kinetic friction has nothing to do with applied force F.
Ex.    3    A block of mass 2kg is placed on the floor. The coefficient of static friction is 0.4.
A force F of 2.5 N is applied on the block, as shown, calculate the force of friction between the block and the floor. (g = 9.8 ms–2)
Sol.        Let R be the normal reaction on the block exerted by the floor. The limiting (maximum) force of static friction is
fs = msR = msmg
= 0.4 x 2kg x 9.8 ms–2 = 7.84 N
The applied force F is 2.5 N, that is less than then the limiting frictional force. Hence under the force F, the block does not move. So long the block does not move, the (adjustable) frictional force is always equal to the applied force. Thus the frictional force is 2.5 N
Ex.4    A heavy box of mass 20 kg is placed on a horizontal surface. If coefficient of kinetic friction between the box and the horizontal surface is 0.25, calculate the force of kinetic friction. Also, calculate acceleration produced under a force of 98 N applied horizontally ?
Sol.        Here, m = 20 kg, µ = 0.25, F = ?, P = 98 N, a = ?
F = µR = µmg = 0.25 × 20 × 9.8 = 49N
Force that produces acceleration
f = P – F = 98 – 49 = 49 N
a =  =  = 2.45 m/s2.

NCERT QUESTIONS WITH SOLUTIONS

Q.1    Fill in the blanks
(a) Friction opposes the ................... between the surfaces in contact with each other.
(b) Friction depends on the ................... of surfaces.
(c) Friction produces ................
(d) Sprinkling of powder on the carrom board ................... friction.
(e) Sliding friction is ................... then, the static friction.
Ans.    (a) relative motion     (b) nature    (c) heat    (d) reduces    (e) less

Q.2    Four children were asked to arrange forces due to rolling, static and sliding frictions in a decreasing order. Their arrangements are given below. Choose the Correct arrangement:
(A) rolling, static, sliding             (B) rolling, sliding, static
(C) static, sliding, rolling             (D) sliding, static, rolling
Ans.    (C) Static, sliding, rolling.

Q.3    Alida runs her toy car on dry marble floor, wet marble floor, newspaper and towel spread on the floor. The force of friction acting on the car on different surfaces in increasing order will be
(A) wet marble floor, dry marble floor, newspaper, towel.
(B) newspaper, towel, dry marble floor, wet marble floor.
(C) towel, newspaper, dry marble floor, wet marble floor.
(D) wet marble floor, dry marble floor, towel, newspaper.
Ans.    (A) wet marble floor, dry marble floor, newspaper, towel

Q.4    Suppose your writing desk is tilted a little, a book kept on it starts sliding down. Show the direction of frictional force acting on it.
Ans.    The book moves downwards. The frictional force is acting opposite to the movement of book.
So it acts upwards.

Q.5    You spill a bucket of soapy water on a marble floor accidently. Would it make it easier or more difficult for you on the floor, Why?
Ans.    The layer of soap makes floor smooth due to which the friction is reduced and the foot cannot make a proper grip on the floor. Therefore it is difficult to walk on a soapy floor and we start to slip on the floor.

Q.6    Explain why sportsmen use shoes with spikes.
Ans.    Sportsmen use shoes with spike to increase the friction between shoes and surface. The shoes with spike do not slip while they run or play.

Q.7    Iqbal has to push a lighter box and Seema has to push a similar heavier box on the same floor. Who will have to apply a larger force and why?
Ans.    The heavy object will be pressed hard against the opposite surface and produces more friction.
So Seema will have to apply a larger force due to more friction.

Q.8    Explain why sliding friction is less than static friction.
Ans.    The two sliding objects find less time to get interlocked against each other (objects and irregularities of surface). So they get less friction. Therefore sliding friction is always less than static friction.

Q.9    Give examples to show that friction is both a friend and a foe.
Ans.    Example to show that friction is a friend and a foe:
Friction is friend
(i) Friction allows us to grip and catch different objects.
(ii) It helps us to walk comfortably on the surface.
(iii) It helps to minimize the speed or to stop the moving objects.
(iv) It helps us to write on paper or blackboard.
(v) The things do not move  from their places due to friction.
Friction is foe
(i) Friction causes wear and tear in objects.
(ii) It causes damage the parts of machines.
(iii) The machines or tools require regular maintenance  due to which a lot of money is wasted.
(iv) It reduces the speed of moving objects so more force is required.
(v) It does not allow the free movement of objects.

Q.10    Explain why objects moving in fluids must have special shapes.
Ans.    The object moving is fluids must have a special shape. This type of shape is called streamlined shape. The streamlined shape helps to overcome the friction between objects and fluids. The objects have pointed fronts with little broader middle portion which gets tapered at the back.

EXERCISE - I

Q.1    Define friction.
Q.2    What is meant by sliding friction ?
Q.3    What is rolling friction ?
Q.4    What is meant by air resistance ?
Q.5    When does static friction come into play ?
Q.6    Which force is responsible for wear and tear of machinery ?
Q.7    Which is greater–rolling friction or sliding friction?
Q.8    What are lubricants ?
Q.9    What are fluids ?
Q.10    Do fluids exert friction ?
Q.11    You spill a bucket of soapy water on a marble floor accidently. Would it make easier or more difficult for you to walk on the floor? Why
Q.12    Explain why sportsmen use shoes with spikes.
Q.13    Iqbal has to push a lighter box and Same has to push a similar heavier box on the same floor. Who will have to apply a larger force and why?
Q.14    Explain why sliding friction is less than static friction.
Q.15    Explain why objects moving in fluids must have special shapes.
Q.16    Why are the soles of shoes grooved ?
Q.17    Give examples to show that friction is both a friend and a foe.
Q.18    Why does friction increase if the two surfaces are pressed ?
Q.19    A labourer has to push a heavy trunk. What should be do to reduce his effort in pushing it and why ?
Q.20    Why is friction essential ? Give three examples.
Q.21    Give five examples to show that friction is increased deliberately.
Q.22    Why are heat resistant tiles laid along the surface of spaceships ?
Q.23    What is meant by lubrication ? Why do we lubricate the moving parts of our vehicles? Name some lubricants and where they are used.
Q.24    What is meant by “streamlined shape” ? Where and why is this shape used ? To whom has nature provided streamlined body?
Q.25    Name the natural force that show down a moving body.
Q.26    Give two advantage of friction.
Q.27    Give two disadvantages of friction.

EXERCISE - II

Q.1    Force of friction is directly proportional to
(A) size
(B) area
(C) weight
(D) all these factors of the moving body

Q.2    Which of the following is the least ?
(A) static friction
(B) sliding friction
(C) rolling friction
(D) limiting friction

Q.3    Friction between two flat surface can be reduced by,
(A) greasing
(B) using ball bearing
(C) decreasing the area
(D) All of the above

Q.4    The flying machine offering the least frictional force should be
(A) irregular
(B) tree-like
(C) symmetrical with many arms
(D) streamlined

Q.5    Frictional force increases with the increase in
(A) roughness of the surface
(B) smoothness of the surface
(C) distance between two bodies
(D) none of these

Q.6    Lubrication of moving surfaces
(A) removes friction
(B) reduces friction
(C) increases friction
(D) has no effect on friction

Q.7    Frictional force is due to ..... between two moving surfaces
(A) softness
(B) roughness
(C) distance
(D) none of these

Q.8    The maximum value of force required to make the body just to slide is known as
(A) dynamic friction
(B) static friction
(C) limiting friction
(D) rolling friction

Q.9    Rolling friction is always more than the
(A) dynamic friction
(B) static friction
(C) limiting friction
(D) none of these

Q.10    What can you use to reduce the force of friction on an object ?
(A) Lubricate the surface
(B) Streamline the body shape
(C) Reduce the surface area in contact of two bodies
(D) All of these

Q.11    Which of the statement is correct about rolling and sliding friction ?
(A) Rolling friction is greater than sliding friction
(B) Rolling friction is lesser than sliding friction
(C) Rolling and sliding frictions acting on a body are equal
(D) None of these

Q.12    A body will experience the minimum friction
in –
(A) Vacuum    (B) Air
(C) Fresh water    (D) Sea water

Q.13    Ball bearings are used to
(A) increase surface area
(B) decrease surface area
(C) increase friction
(D) decrease friction

Q.14    Lubricants are used to
(A) reduce friction
(B) increase friction
(C) make a surface shiny
(D) make a surface oily

Q.15    SI unit of force of friction is
(A) N        (B) kg wt
(C) kg ms–2    (D) Joule

Q.16    Ball bearings are used to
(A) increase friction
(B) decrease friction
(C) optimize friction
(D) remain same

Q.17    The use of lubricants makes the surface
(A) smooth    (B) rough
(C) very rough    (D) no effect

Q.18    The frictional force ...... with the ......... in roughness of the surfaces
(A) increases, increase
(B) decrease, decrease
(C) decrease, increase
(D) increases, decrease
Q.19    The maximum force of friction when the body is just beginning to move is known as the
(A) limiting friction
(B) rolling friction
(C) static friction
(D) none of these

Q.20    The friction that exists between a surface sliding on another surface is called the
(A) dynamic friction
(B) rolling friction
(C) static friction
(D) none of these

1.    D    2.    C    3.    D    4.    D
5.    A    6.    B    7.    B    8.    C
9.    D    10.    D    11.    B    12.    A
13.    B, D    14.    A    15.    A    16.    B
17.    A    18.    A    19.    A    20.    A

EXERCISE - III

Tick (P) the correct choice among the following :
1.    Impulse is
(A) a scalar quantity         (B) a vector quantity
(C) neither a scalar nor a vector     (D) sometimes a scalar and sometimes a vector
2.    Choose the wrong statement:
(A) 1 kg wt = 9.8 N
(B) Momentum is a vector quantity
(C) Force is always conserved
(D) Momentum is conserved in the absence of an external force
3.    A long-jumper runs before jumping because
(A) he covers a greater distance     (B) he maintains momentum conservation
(C) he gains energy by running     (D) he gains momentum
4.    If a rock is brought from the surface of the moon
(A) its mass will change         (B) its weight will change, but not mass
(C) both mass and weight will change     (D) its mass and weight will remain the same
5.    If 1 kg wt = 10 N, the value of gravitational intensity will be
(A) 10 m/s2     (B)  m/s2    (C) I m/s2     (D)  m/s2
6.    The force acting on a mass of 1 g due to the gravitational pull on the earth is called 1 gwt. One gwt equals
(A) 1 N     (B) 9.8 N     (C) 980 dyne     (D) none of these
7.    A man is standing on a boat in still water. If he walks towards the shore the boat will
(A) move away from the shore     (B) remain stationary
(C) move towards the shore    (D) sink
8.    A driver accelerates his car first at the rate of 1.8 m/s2 and then at the rate of 1.2 m/s2. The ratio of the forces exerted by the engines will be respectively equal to
(A) 2 : 3     (B) 1 : 2     (C) 2 : 1     (D) 3 : 2
9.    A body of mass 5 kg undergoes a change in speed from 30 to 40 m/s. Its momentum would increase by
(A) 50 kg m/s     (B) 75 kg m/s     (C) 150 kg m/s     (D) 350 kg m/s
10.    The force needed to produce an acceleration of 6 m/s2 in a ball of mass 4 kg will be
(A) 24 N     (B) 30 N     (C) 32 N     (D) 36 N
11.    A body of mass 5 kg undergoes a change in speed from 20 to 0.20 m/s. The momentum of the body would
(A) increase by 99 kgm/s     (B) decrease by 99 kgm/s
(C) increase by 101 kgm/s     (D) decrease by 101 kgm/s
12.    A bullet of mass 0.01 kg is fired from a gun weighing 5.0 kg. If the initial speed of the bullet is 250 m/s, calculate the speed with which the gun recoils.
(A) – 0.50 m/s     (C) – 0.25 m/s     (B) + 0.05 m/s     (D) + 0.25 m/s
13.    A body of mass 100 g is moving with a velocity of 15 m/s. The momentum associated with the ball will be
(A) 0.5 kgm/s     (B) 1.5 kgm/s     (C) 2.5 kgm/s    (D) 3.2 N s
14.    A stationary ball weighing 0.25 kg acquires a speed of 10 m/s when hit by a hockey stick. The impulse imparted to the ball is
(A) 2.5 N s     (B) 2.0 N s     (C) 1.5 N s     (D) 0.5 N s
15.    The combined effect of mass and velocity is taken into account by a physical quantity called
(A) torque     (B) moment of force     (C) momentum
(D) moment of momentum
16.    Momentum has the same units as that of
(A) impulse     (B) torque
(C) moment of momentum(D) couple
17.    A hammer weighing 3 kg, moving with a velocity of 10 m/s, strikes against the head of a spike and drives it into a block of wood. If the hammer comes to rest in 0.025 s, the impulse associated with the ball will be
(A) 30 N s     (B) – 30 N s     (C) 15 N s     (D) –15 N s
18.    In the above problem, the average (retarding) force acting on the spike will be
(A) 600 N     (B) – 600 N     (C) 1200 N     (D) – 1200 N
19.    A rocket works on the
(A) first law of motion         (B) second law of motion
(C) third law of motion         (D) law of conservation of energy
20.    A metallic ball strikes a wall and falls down whereas a tennis ball having the same mass and same velocity bounces back. The reason for this is that
(A) both suffer equal change in momentum
(B) the tennis ball suffers a greater change in momentum
(C) metallic ball suffers a grater change in momentum
(D) the momentum of the tennis ball is less than that of the metallic ball.
21.    When a bicycle travels on a rough surface, its speed
(A) increases     (B) decreases     (C) remains the same     (D) none of these
22.    It is difficult to walk on ice because of
(A) absence of friction     (B) absence of inertia     (C) more inertia     (D) more friction
23.    The law which defines force is
(A) Newton's third law of motion     (B) Newton's first law of motion
(C) Newton's second law of motion     (D) Newton's law of gravitation
24.    Friction between any two objects is due to
(A) attraction between them     (B) repulsion between them
(C) some adhesive forces between them     (D) irregularities on the surfaces
25.    Which of the following class of forces is different from others?
(A) pulling of a cart         (B) stretching of a coiled spring
(C) kicking of a football     (D) electrical force
26.    Which of the following class of forces is different from others?
(A) magnetic force     (B) electrical force    (C) gravitational force     (D) Stretching of a spring
27.    If g = 10 ms–2, what is the force of gravity acting on a mass of 1 kg?
(A) 1 N     (B) 10 N    (C)  N     (D) none of these
28.    1 dyne is equal to
(A) 980 g wt     (B) 98 g wt     (C) 980 kg wt     (D) none of these
29.    The effect of an impulse force on the body is measured only in terms of its
(A) force
(B) moment of momentum     (C) impulse
(D) none of these
30.    kg ms–1 is the SI unit of
(A) impulse     (B) force     (C) angular velocity     (D) none of these
31.    Galileo's law of inertia is another name for newton's law of motion.
(A) first     (B) second     (C) third     (D) anyone of the above
32.    Graphite powder is used in machines to
(A) enhance friction     (B) enhance profit     (C) reduce friction     (D) reduce efficiency
33.    Friction force is a
(a) self-adjusting force         (B) necessary evil
(C) important force in daily life    (D) all the above
34.    A diwali rocket is ejecting 0.05 kg of gases per second with a velocity of 400 ms–1. The accelerating force on the rocket is
(A) 20 dyne     (B) 20 newton     (C) 20 kg wt    (D) sufficient data not given
35.    If the mass of a body is 12.1 g and the density is 2.2 g/cc, its volume is
(A) 5.5 cm3     (B) 8 cc    (C) 11 cc     (D) 55 cc
36.    Aluminium has a density of 2.7 g/cc. The mass of 15 cc of aluminium is
(A) 45 g     (B) 40.5 g     (C) 80 g     (D) 100 g
37.    The buoyant force depends on the
(A) depth of a liquid     (B) density of a liquid    (C) colour of a liquid    (D) none of these
38.    The hot air balloon rises because it is
(A) denser         (B) less dense
(C) equally dense         (D) the given statement is wrong
39.    A force of 50 N is applied on a nail of area 0.001 sq. cm. Then the thrust is
(A) 50 N     (B) 100 N     (C) 0.05 N     (D) 10 N
40.    The SI unit of thrust is
(A) N     (B) dyne    (C) kg wt     (D) N m–2
41.    Pascal is the unit for
(A) pressure     (B) thrust     (C) buoyant force     (D) none of these
42.    1 millibar is equal to
(A) 100 N m–2     (B) 10 N m–2     (C) 1 N m–2     (D)  N m–2
43.    An object of mass 10 g acquires a speed of 100 ms–1 in travelling through a distance of 50 cm. If the force acting on the object is constant, its magnitude will be
(A) 1 newton     (B) 10 newton     (C) 100 newton     (D) 1000 newton
44.    The resultant of two opposite vectors is equal to
(A) the sum of the two.     (B) the difference of the two
(C) the product of the two.     (D) the ratio of the two.
45.    A ball of mass 1 kg moving horizontally due North at 8 m/s strikes a vertical wall and is reflected back with a speed of 6 m/s. The change in its momentum is
(A) 14 kg m/s     (B) 8 kg m/s     (C) 6 kg m/s     (D) 2 kg m/s
46.    An object of mass 10 g acquires a speed of 100 m/s after 1 second. If the force acting on the object is constant, its magnitude will be
(A) 1 N     (B) 10 N     (C) 100 N     (D) 1000 N
47.    If a hole is bored along the diameter of earth and a stone is dropped into the hole
(A) The stone reaches the centre of the earth and stops there.
(B) The stone reaches the other side of the earth and stops there.
(C) The stone executes simple harmonic motion about the centre of the earth.
(D) The stone reaches the other side of the earth and escapes into space.
48.    The force F acting on a body moving in a circle of radius r is always perpendicular to velocity v. The work done by the force on the body is
(A) Fv     (B) Fr     (C) 2Fr     (D) zero
49.    The momentum of a body of mass 5 kg is 15 kg m/s. Its kinetic energy is
(A) 10 joule     (B) 20 joule     (C) 22.5 joule     (D) 25 joule
50.    A particle moves in a circle of radius r with a constant speed under a centripetal force f. The work done in completing a full circle is
(A) 2 rf     (B) pr2 f     (C) 2 p rf     (D) zero
51.    A ball X is dropped freely under gravity from a height. Another ball Y is projected horizontally from the same point.
(A) X will reach the ground first     (B) Y will reach the ground fust
(C) Both will reach simultaneously     (D) Y will never reach the earth
52.    The length of a second's pendulum on the surface of earth is 1 m. The length of the second's pendulum on the surface of moon where g is l/6th that of the value on earth will be
(A) 36 m     (B) 6 m     (C) m    (D) m
53.    A force of 21.0 N acts on a particle of mass 3.0 kg in a medium whose resistance is 2.0 N/kg. The acceleration of the particle is
(A) 5.00 m/s2     (B) 7.00 m/s2     (C) 7.66 m/s2     (D) 9.00 m/s2
54.    Two bodies, one light and the other heavy, have equal momentum. Which of them has greater kinetic energy?
(A) The heavy body         (B) The light body
(C) Both have equal kinetic energies     (D) Depends upon the direction of the momentum
55.    A brick at rest on a horizontal table is pulled by a horizontal cord. The force of friction on the brick

(A) increases if the pull increases but the brick does not move.
(B) is directed horizontal to the right.
(C) decreases if an identical brick is placed on the first.
(D) is zero if the brick is pulled hard enough to make it slide.
56.    A body of mass m slides down an inclined plane of 45°. If the coefficient of friction between the body and the plane be 0.3, the acceleration of the body is
(A) 0.22 g     (B) 0.30 g     (C) 0.49 g     (D) 0.70 g
57.    An object of mass 10g acquires a speed of 100 m/s in travelling through a distance of 50 cm. The magnitude of force acting on the body is
(A) 1 newton     (B) 10 newton     (C) 100 newton     (D) 1000 newton.
58.    A force of 2 newton will produce in a body of mass 1kg
(A) speed of 1 m/s         (B) speed of 2m/s
(C) acceleration of 1 m/s2     (D) acceleration of 2m/s2
59.    Newton's third law, action and reaction
(A) act on the same object.     (B) may act on different objects.
(C) must act on different objects.
(D) must be equal in magnitude and should act in the same direction.
60.    The law which defines the force is
(A) Newton's third law of motion.     (B) Newton's second law of motion.
(C) Newton's first law of motion.     (D) Law of conservation of linear momentum.
61.    Impulse is equal to
(A) the change in momentum.     (B) the rate of change of momentum.
(C) the product of mass and velocity.     (D) the product of force and velocity.
62.    The force of friction is
(A) dependent on the area in contact.     (B) independent on the nature of surfaces in contact.
(C) dependent on the nature of surfaces in contact.
(D) dependent upon the direction of external force.
63.    Recoiling of gun can be explained on
(A) Newton's first law of motion.     (B) Newton's second law of motion.
(C) Law of conservation of linear momentum.     (D) the basis of balanced forces.
64.    A planet whose mass and radius is half of the earth, the acceleration due to gravity on its surface is
(A) 19.6m/s2     (B) 9.8m/s2     (C) 4.9m/s2     (D) 2.45m/s2
65.    A stone is dropped from the roof of a house and is found to reach the ground in one second. The height of the house is
(A) 4.9m     (B) 9.8m     (C) 12m     (D) 19.6m