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Question-1

What force would be needed to produce an acceleration of 4m/s2 in a ball of mass 6kg?

Solution:
To be calculated : Force, F= ?
Mass, m = 6 kg
And, Acceleration, a = 4m/s2
Now, putting these values of m and a in the equation:
F = m x a
F = 6 x 4
Force, F = 24 N
Thus the force needed is of 24 newtons.

Question-2

A force acts on an object which is free to move. If we know the magnitude of the force and the mass of the object, which aspect of motion of the object does Newton’s second law of motion enable us to determine?

Solution:
Newton’s second law enables us to determine the acceleration of the object, if we know the magnitude of the force and the mass of the object.

Question-3

When force applied by a moving vehicle is calculated, the actual force applied by the brakes may be slightly less than the one calculated theoretically. Why?

Solution:
The actual force applied by a moving vehicle is slightly less than the one calculated theoretically because of opposing forces of friction.

Question-4

When can we say that one body interacts with the second body?

Solution:
When one body influences another body by applying force, we say that the first body interacts with the second body.

Question-5

Define the force of friction.

Solution:
The force which always opposes the motion of one body over another body in contact with it is called the force of friction or just friction.

Question-6

How do ball- bearings affect the nature of friction? Illustrate with an example.

Solution:
The ball- bearings reduce friction by converting sliding friction into rolling friction. For example, when the axle of a machine fitted with ball-bearings rotate, then the metal balls also roll and hence the friction is reduced. The free-wheels of bicycles, the axles of cars, the shaft of motors and many other machines are provided with ball-bearings to reduce friction.

Question-7

When does the maximum loss in weight of an object immersed in water take place? Illustrate.

Solution:
The maximum loss in weight of an object takes place when it is fully immersed in a liquid. Consider a body immersed in a liquid. Greater the volume of an object immersed in a liquid, greater is the decrease in the apparent weight of the object and it seems to become more and more lighter. But once the object is completely immersed under the liquid, then further lowering it in liquid does not made it any more lighter. This means that the maximum loss in weight of an object takes place when it is fully immersed in liquid.

Question-8

If two equal weights of unequal volumes are balanced in air, what will happen when they are completely dipped in water?

Solution:
Since the two weights have unequal volumes, they will displace unequal weights of water and hence undergo an unequal loss in weight on being completely dipped in water. The two weights will, therefore become unequal in water and get unbalanced.

Question-9

Two different objects are completely immersed in water and undergo the same loss in weight. Is it necessary that their weights in air should also be the same? Explain.

Solution:
The two different objects completely immersed in water can undergo the same loss in weight only if they displace equal weights of water. And they can displace equal weights of water if they have equal volumes. So, in this case the two different objects should have equal volumes. It is not necessary that their weights in air should be the same. This is because the loss in weight of an object on immersing in water depends on its volume, not on its weight.

Question-10

Give important applications of Archimedes’ principle.

Solution:
The following are the important applications of Archimedes’ principle:

1. Archimedes’ principle is used in determining the relative density of a substance.
2. The hydrometers used for determining the density of liquids are based on Archimedes principle.
3.The lactometers used for determining the purity of milk are based on Archimedes’ principle.
4. Archimedes’ principle is used in designing ships and submarines.

Question-11

What was Galileo’s argument against the old concept of Greek philosophers?

Solution:
Galileo observed that on an inclined plane, the velocity of a body increases when it rolls down and decreases when it climbs up. He argued that on a plane inclined equally on both sides, a marble rolled from one side would attain the same height on the other side. He further argued that if the inclination of the plane on one side were gradually decreased, the marble would have to cover a larger distance to reach the same height and if the plane were made horizontal, the marble would continue to move forever in order to attain the same height. He challenged the age-old concept of Greek philosophers that the natural state of bodies is the state of rest by saying instead that, the natural tendency of bodies is to oppose a change in their state of motion.

Question-12

Why do passengers in the bus fall backward when the bus begins to move suddenly?

Solution:
Initially both the bus and the passengers are at the state of rest. The force applied on the bus by its engine makes it move. A sudden movement results in a change in state of motion of the bus as well as the passenger’s feet in contact with it. But rest of the passenger’s body opposes this change in state of motion due to its inertia and tries to remain where it was. Hence the passengers fall backward when the bus begins to move suddenly.

Question-13

Do all bodies have the same inertia? Explain it with an example.

Solution:
All bodies do not resist a change in their state of motion to the same extent. Some resist more than others. For example, if we give a hard kick to a football, it flies off. But if we kick a stone of same size with an equal force, it may not move at all, rather we injure ourselves. This is because, the inertia of the stone is more than that of the football. Hence more massive an object, greater will be its inertia.

Question-14

How will we derive at the expression for Newton’s second law of motion?

Solution:
Newton’s second law of motion states that the rate of change of momentum of a body is directly proportional to the force and takes place in the same direction as the force. Suppose the velocity of a body of mass m changes from u to v in time t. The magnitude of initial and final momentum of the body will be
p1 = mu ----(1)
and p2 = mv ----(2)

The change in momentum (p2 – p1) takes place in time t. According to Newton’s second law
of motion, the magnitude of the force F is
F

F = k ----(3)
where k is a constant of proportionality. But substituting equation (1) and (2) in (3) we get
F = k
Now is the magnitude of the rate of change of velocity \, which is the acceleration a, so we have
F = kma ----(4)
We can choose the units of force in such a manner that the value of k = 1. If we substitute this value in equation (4), we get

F = ma

The above equation states that the product of its mass and the acceleration determines the force acting on a body.

Question-15

Explain with an example that action and reaction acts on two different bodies.

Solution:
When a person swims in water, he pushes the water backwards with hands and feet to move forward. It is the reaction to this force that pushes him forward. Here the action and reaction acts on two different bodies.

Question-16

Is it true that two bodies can exert force on each other only when they are in contact? If not give an example.

Solution:
It is not necessary that two bodies can exert force on each other only when they are in contact. For example, interaction between a magnet and a piece of iron or between two magnets can take place even without being in contact. A comb charged by rubbing it with dry hair, attracts small bits of paper.

Question-17

Total momentum of a body remains unchanged before and after the collision. Explain.

Solution:
Consider two marbles A and B having masses m1 and m2 respectively. Let the initial velocity of marble A be u1 and that of marble B be u2. Suppose the two marbles collide with each other head on and their collision lasts for t seconds, then the velocities of marbles A and B become v1 and v2 respectively after the collisions, then the momentum of marble A before and after the collisions is m1u1 and m1v1 respectively. The rate of change of momentum during the collision will be . Similarly the rate of change of momentum of marble B will be . If the force exerted by marble A and B is F12 and that by B on A is F21, then according to the second law of motion
F12 = ----(1)
and F21 = ----(2)
According to the third law of motion, the force F12 exerted by marble A on marble B and the force F12 exerted by the marble B on the marble A should be equal and opposite to each other.Therefore,
F12 = -F21
Substituting, the value of F12 and F21 from equations (1) and (2), we get
=
m1(v1 – u1) = m2(v2 – u2)
m1u1 + m2u2 = m1v1 + m2v2

Now (m1u1 + m2v2) is the total momentum of the two marbles before the collision and (m1v1 + m2v2) is their total momentum after the collision. Hence we find that in a collision between the two marbles the total momentum before and after the collision remains unchanged.

Question-18

With an example explain the basis of law of conservation of momentum.

Solution:
When a gun is fired, the bullet leaves the barrel with some velocity, i.e. the bullet has some momentum. The bullet and the gun were at rest before the shot was fired. Therefore, initially the total momentum of both the bullet and gun was zero. When the gun is fired, the bullet acquires certain velocity and therefore some momentum as it leaves the gun. Since the momentum before and after firing should remain conserved, the gun must have momentum equal to that of the bullet, but in opposite direction. The gun therefore moves in a direction opposite to that of the bullet.

Question-19

How does lubrication reduce friction?

Solution:
When a lubricant is used between two moving surfaces, its particles get into the uneven parts of the surfaces and make a thin layer of their own between them. As a result the motion actually takes between the layers of lubricating materials, which are relatively smoother. Similarly when we sprinkle powder on a carom board, the power acts as a lubricant. The depressions on the surface of the board and the coins of carom get filled with the powder. This reduces friction between the board, the striker and the coins of the carom.

Question-20

Give examples where effect of force is increased and decreased? Explain how.

Solution:
Effect of force is increased in tools like knives, axes, pins and nails. The effect of force is increased by decreasing the area on which they act.
Effect force is decreased in the foundation of buildings and dams. In vehicles, additional tyres are provided to carry heavy loads.
The effect of force is decreased by increasing the area.




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