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1. Is it possible for one object to gain mechanical energy from another without
touching it? Explain.
Answer: Yes. It is possible for one object to gain mechanical energy from another
without touching it.
Consider following few examples.
a) GRAVITATION:
Recall Newton’s law of gravitation.
The force of attraction between the two bodies is given by
mm
F  G 12 2
r
Hence when any object is released from some height, it automatically gains the
kinetic energy because of Earth’s gravitational force acting on it and it approaches
the ground. In this case, initially, there is obviously no contact between the object
and the earth.
In this case, the object is in the gravitational field of the Earth and hence it has
gravitational potential energy due to earth’s gravitational field. When released, this
gravitational potential energy gets converted into kinetic energy.
b) ELECTROSTATICS:
Recall Coulomb’s law in Electrostatics, of the force between the two electric
charges.
The force of attraction between the two charges is given by
qq
F  K 12 2
r
where K is a constant of proportionality.
Now, if the charges are placed in vacuum, the equation becomes
1 q 1q 2
where the symbols have their usual meanings.
F
4 0 r 2
Consider two charged particles charges of 1 coulomb.
Both the charges are +ve. If the charges are held at some finite distance, these
charges will repel each other. But if released, both the charges will move away from
each other, because of repulsive force.
In this case, each charge is in electric field of another one. Hence Each charge has
some finite potential energy because of presence of the other. This potential energy
gets converted into kinetic energy, and the charges depart.
c) Magnetism: On the parallel ground, think of what would happen in case, if a north
or south pole of one magnet is brought near N/S pole of another magnet. Without
touching, the magnets will experience the force of Repulsion/Attraction depending
on the poles facing each other.
2. A ball is thrown straight upward on the Moon. Is the maximum height it reaches
less than, equal to, or greater than the maximum height reached by a ball
thrown upward on the Earth with the same initial speed (no air resistance in
both cases)? Explain.
Answer:
Consider the third kinematical equation,
v2 = u2 + 2as --- (1)
where u – initial velocity,
v –velocity after traveling distance s.
a – acceleration.
For vertically upward motion, the gravitational acceleration (g) acts as a retardation and
therefore is to be taken as –ve.
Then equation (1) gives
v2 = u2 – 2gh --- (2)
When the ball attains maximum height i.e. Hmax, its velocity v = 0.
Then eqn (2) gives,
0= u2 – 2gHmax
i.e.
u2 =2gHmax
The maximum height attained
ON EARTH H max 
u2
2g
------ (4)
On MOON:
th
1
The gravitational acceleration of the moon (say gm) is   that of the Earth.
6
g
i.e. g m 
6
 u2 
The maximum height attained ON MOON h max  6 
 2g 
h max  6H max for the same initial speed.
i.e.
i.e. The maximum height attained on the Moon will be 6 times that on the Earth
for the same initial speed, i.e. greater than that attained on the earth.
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