67. A
steel ball is floating in a trough of mercury. If we fill the
empty part of the trough with water, what will happens to the
steel ball?
The steel ball floats in the mercury because it's less dense than mercury. However it's denser than the water. In case if it is immersed in the water, it gets sunk in it. But here the case is something else. Here a part of it is in the mercury while a part is in water. due to the density of mercury, it floats on it as it gets some upthrust and when water is poured over the setup, then it gets some additional upthrust from water too. Due to this the steel gets raised to some extent however it's not floated in the water due to its density.
68. A piece
of ice floats on water. What will happen to the level of
water when the ice melts completely?
The floating of ice or any other body
is governed by the principle of floatation which states that the weight of the floating body is equal to the weight of the liquid displaced by it. So the sunken portion of the ice displaces some amount of the water. And the weight of that amount of water is equal to the wholesome weight of the ice floating in it.
When ice melts giving water, the system does not get
any thing from outside, no addition, no subtraction. So the
weight of the displaced water is same, i.e. there will be no
rise or fall in the level.
69.
A piece of
ice is floating inside a vessel containing water and inside the
ice is a bubble of air. Will the level of water in the vessel be
altered when the ice melts?
The floating of ice is governed
by the principle of floatation which states that the weight
of the floating body is equal to the weight of the liquid
displaced by it. So the sunken portion of the ice plus air
bubble displaces some amount of the water. And the weight of
that amount of water is equal to the wholesome weight of the
ice plus air inside air bubble. When ice melts giving water
the air enclosed inside air bubble escapes from it. As a
result, the level of the water in the vessel falls. So,
there is alteration in the level of the vessel when the ice
melts.
70. A man is sitting in a boat floating in a pond. If the drinks some
water from the pond, what will happen the level of water in the
pond?
A
man sitting in a boat floating in a pond & if he drinks some
water from the pond then the level of water will not change. On drinking the water (say m gm), the man displaces
some more water equivalent to 'm' gm tending to raise the level.
But this much amount of water had
just been used. Since the addition and deduction of water is
same, the level of water will be same.
71. When air is blown in between two balls suspended close to each other, they are attracted towards each other. Why?
When the air blows the balls, the velocity
of air increases and hence according to Bernoulli's Law, the
pressure there will decrease compared to other regions. So
the balls will face an inner directing force from other
regions and they seem to attract each other.
When the suspended balls were in the undisturbed condition, there was some amount of pressure exerted by the air on the balls which exists due to the existence of the air in the atmosphere. When the air is blown between the balls, the velocity of the air in between increases and the pressure decreases. There is a creation of a partial vacuum in between the balls so to fill the space the balls move towards each other.
Hence,
when air is blown in between two balls suspended close to
each other, they are attracted towards each other.
72. A balloon filled with Helium does not rise in air indefinitely. Why?
The balloon filled with helium doesn't rise indefinitely because the helium is a slightly denser gas than the hydrogen which is usually filled in the balloons. It’s density is near to the density of the atmospheric air. And as the height increases or as we go up from the earth surface, the atmosphere becomes rarer. So at some height, the density of the air becomes equal to the density of the helium gas filled in the balloon.
Thus that forms a homogeneous system. And the air can no longer provide the upthrust to the balloon filled with helium because only the denser medium can provide upthrust to the body rarer than the medium. So after attaining equilibrium, the balloon will neither rise nor falls.
73. Ice floats in water with about nine-tenth of its volume submerged. What is the friction volume submerged for an iceberg floating on a fresh water lake of a (hypothetical) planet whose gravity is ten times that of that of the earth?
According to the principle of floatation, any floating object displaces the amount of liquid (in which it’s floating) which is equal to it’s own weight.
In case of the ice here, nine-tenth fraction of its volume is under the water. So that much amount of water is displaced. Thus the wholesome weight of the ice is given by that amount of water.
We can write it as 9/10V g=mg (where 9/10V is the fractional volume of the submerged ice, is the density of the liquid, m is the mass of the ice and g is the acceleration due to gravity.). On analyzing, we see that 9/10V=m/ . Thus the fractional volume of the floating object is found to be independent of the acceleration due to gravity. Even though the weight of the floating object and the amount of water displaced by the submerged portion changes. But the net effect is neutral on the fractional volume. Thus no change is seen in the fractional submerged volume of ice on such planet provided that the mass of ice taken is of same mass and the density of the liquid used be equal to the density of water on earth.
74. A bucket containing water is rotated in a vertical circle. Why does not water fall?
A bucket containing water is rotated in a vertical circle.
The water does not fall because the weight of the water is
balanced by centrifugal force. When the bucket containing
water is rotated in a vertical circle then centripetal as
well as centrifugal forces come into play. When the bucket
is upside-down then the tension T will be minimum and the
resultant of the tension and total weight of bucket plus
water becomes equal to centripetal force whose direction is
always towards the center of that circular motion. At the
instant, the centripetal force is balanced by centrifugal
force whose magnitude is equal to that of the centripetal
force and direction is always opposite to that of the
centripetal force. Hence, fall of water from bucket is
prevented by the balanced in the centripetal & centrifugal
force. As a result, water does not fall.
75. Why does banking a pilot not fall
down, when the aeroplane loops a vertical loop?
By banking a pilot does not fall down even when the
aeroplane loops a vertical loop. It is because the weight of
the plane plus pilot is balanced by centrifugal force as the
motion of aeroplane during banking is circular motion where
centripetal as well as centrifugal forces come into play.
When the pilot is upside-down then the resultant of the
tension and total weight of aeroplane plus pilot becomes
equal to centripetal force whose direction is always towards
the center of that circular motion which is opposed by
centrifugal force whose magnitude is equal to that of the
centripetal force. Hence, falling of pilot from aeroplane is
prevented by the balanced in the centripetal & centrifugal
force. As a result, a pilot does not fall down even when the
aeroplane loops a vertical loop.
76. How does banking of road reduce wear and tear of the tires?
If the roads
are not banked then the centripetal force for circular
motion is provided by the sidewise frictional force exerted
by the road on the tyres which causes the wear & tear of the
tyres.
When
the roads are banked where it takes a curve then the normal
reaction of the vehicles splits into two components i.e.
vertical component & horizontal component. The vertical
component balances the weight of that vehicle & the
horizontal component provides necessary centripetal force
for uniform circular motion. As a result, no sideways
frictional force comes into play to provide centripetal
force as the necessary centripetal force is already provided
by the horizontal component of normal reaction. So, there is
no wear & tear of the tyres when the roads are banked.
77. Why are passengers of a car rounding a curve thrown outward?
As the force
acting on passengers of a moving car is always opposite to
the direction in which acceleration of the car acts. When a
car is rounding a curve then the centripetal force acts on
that car & direction of centripetal acceleration is towards
the center of a car. Hence, the force acting on the
passengers of a car is away from the center. So, passengers
of a car rounding a curve are thrown outward.
78. What will provides necessary centripetal force to car taking turn on a level road?
If the roads are not banked then the
centripetal force for circular motion is provided by the
sidewise frictional force exerted by the road on the
tyres.
When
the roads are banked where it takes a curve then the
normal reaction of the vehicles splits into two
components i.e. vertical component & horizontal
component. The vertical component balances the weight of
that vehicle & the horizontal component provides
necessary centripetal force to car taking turn on a
level road.
79. Curved
railway tracks are banked. Why?
If the curved
railway tracks are not banked then the centripetal force for
circular motion is provided by the rails exerting a sidewise
force on the inner rims of the wheel which may cause
dangerous accident which may take thousands of lifes.
When
the curved railway tracks are banked then the normal
reaction of the train splits into two components i.e.
vertical component & horizontal component. The vertical
component balances the weight of train & the horizontal
component provides necessary centripetal force for uniform
circular motion. As a result, no sideways frictional force
comes into play to provide centripetal force as the
necessary centripetal force is already provided by the
horizontal component of normal reaction of train. In order
to prevent accident & to provide safe driving, curved
railway tracks are banked.
80. The handle of a screw is made wide, why?
In rotational
dynamics, the torque required for revolution is defined as
the product of the force F and the perpendicular distance
from the axis of rotation
i.e. T =
Fr.
To produce a given turning effect, if the distance from the
axis of rotation r is large, less force
F will be enough. Hence, the handle of the screw is made wide.