Define the terms force, inertia and momentum.

(i) Any external imbalance that changes or tends to change the state of rest or uniform motion in a straight line or the direction of motion is called as Force. 

Force always produces acceleration in the body. 

(ii) Inertia is the ability of the body to change the state of rest or uniform motion, unless acted upon by an external force. 

Inertia is categorized into three types:

i) Inertia of rest,
ii) Inertia of motion, and
iii) Inertia of direction.

Inertia of rest: It is the property of body by virtue of which it cannot change the state of rest by itself. 

Inertia of motion: It is the tendency of the body to remain in the state of uniform motion in a straight line. 

Inertia of direction: It is the property of body by virtue of which it cannot change the direction of motion by itself.

(iii) Momentum is a measure of the quantity of motion contained in the body and is equal to the product of mass and velocity.

Momentum is a vector quantity and it's direction is same as that of velocity.

Mathematically, momentum is given by,

                    

(a)  

The true weight of body = Mg

Reaction of floor = R

Net force acting on the body is,

                     F = Mg  - R

If a is the acceleration with which lift moves downward, then

                     F = M a

∴                Ma = Mg - R

i.e.,               R = M(g - a)

Thus the apparent weight of the body is,

                 

(b)

If lift is ascending in upward direction with acceleration a then

                 Ma = R - Mg

or                

(c)  

If lift moves with constant velocity then acceleration, a = 0. 

∴                

So, reading on the machine = Mg

Ans.

(i) For ,

The force acting on the body is constant. Thus,  the body has uniform accelerated motion.

(ii) For,

Force on the body is zero, therefore body has uniform motion. 

(iii) For , 

The force is negative and increases linearly with time in magnitude, thus the motion is non-uniformly retarded motion.

(iv) For ,

The force is positive and increases linearly with time, thus the motion is non-uniformly accelerated motion.

(v) For ,

The force acting on the body is constant, thus the body has uniform accelerated motion.

(vi) For ,

The force acting on the body is constant and negative, thus the body has uniformly retarded motion.

Law of conservation of momentum:
It states that total momentum of system remains conserved in the absence of external force.

Second law is the real law of motion. This can be proved by showing that first law and third law are contained in second law of motion.
(i) First law is contained in second law. According to the second law of motion,

                                     
                               
That is if no force is acting on the body then its acceleration is zero, means if a body is at rest, it remains at rest and if the body is moving in straight line with constant velocity, it continues to do so. This is what the first law states. Hence first law is contained in the second law.
(ii) Third law is contained in second. According to the second law of motion,