101. When a man
standing on a turntable suddenly drops his hands to his height,
the table moves faster. Why?
According to the law of conservation of angular momentum, "if
no external torque is applied on the system then the angular
momentum of that system remains constant" i.e. the
system will always try to keep the angular momentum
conserved
().
By dropping the hands, the moment of inertia I will be
decreased. In the absence of external torque, the angular
velocity must increase. Hence,
when a man standing on a turntable suddenly drops his hands
to his height, the table moves faster.
102. Which wrench
are more usefula wrenches if shorter arm or those of longer
arm?
If r_{1}
& r_{2} be the length of the arm of longer wrench &
shorter wrench respectively then
t_{1}
&
t_{2}
are
respective torques observed with the same force F applied on
them. Here,t_{1
}
= r_{1.} F &
t_{2
}
= r_{2.} F. As
r_{2} > r_{1 }so,
t_{2 }
>
t_{1 }
i.e. the turning affects on the
long wrench is much greater than that on the short wrench. So, the
longer arm wrench is more useful.
103. A girl sits
near the edge of a circular platform rotating with a uniform
angular velocity . What change will be observed in the emotion
of the platform?
According to
the law of conservation of angular momentum, "if no external
torque is applied on the system then the angular momentum of
that system remains constant". The
system will always tries to keep the angular momentum
conserved
(). In the presence of the girl, the moment of inertia I will
be increased so, angular
velocity has to
be decreased i.e. the platform will rotates slowly.
104. A helicopter
has two propellers. Why?
According to
the law of conservation of angular momentum, "if no external
torque is applied on the system then the angular momentum of
that system remains constant". The
system will always tries to keep the angular momentum
conserved
(). If
there were only one propeller, the helicopter itself would
have turned in opposite direction & cannot conserve its
angular momentum. In order to conserve the angular momentum,
a helicopter has two propellers.
105. The bicycles
have large diameter wheels. What is its important that the tyres
be light weighing?
Due to large diameter
wheels in the bicycles, the moment of inertia M.I. will be high though mass is
small and the angular spin will be smaller. Further, if the
mass is increased, more force will be required to accelerate
to a given rate. Hence, bicycles have large diameter wheels and
light weight.
106. The front end
of the car raises little when it is accelerated rapidly, why?
The frictional force
provided by the contact of the tyres of car with the ground accelerates a car
pointing forward. This exerts a torque that tends to rotate
its back end down ward and its front upward. Hence, the front
end of the car raises little when it is accelerated rapidly.
107. Fly wheel is
used in railway engine. Why?
The flywheel is a large heavy wheel with a long cylindrical
axle passing through its center of mass lying on the axis of
rotation. It is constructed in such a way that most of the
mass is concentrated at the rim. This increases the value of
moment of inertia i.e. I. This moment of inertia opposes any change in uniform rotators. Hence, when
the flywheel is attached with the engine. It assures the
running of engine smoother and steadier.
108. People with
long legs generally walk with a slower stride than people with
short legs. Why?
Every
system will try to keep the angular momentum
conserved
& angular momentum is given by the relation:
(where I is moment of inertia &
w
be the
angular velocity). People with long legs generally walk with
a slower stride than people with short legs.
This is because short legs have less rotational inertia (i.e.
I) than
long legs. So, for a same angular momentum, people with long
legs generally walk with a slower stride than people with
short legs.
109. A disc of
metal is recast in the form of a solid sphere. What will
happens to the M.I. about a vertical axis passing through the
center?
For the disc, the
moment of inertia M.I. about a vertical axis passing through
center is given by the relation:
Where, M is
the mass of the sphere. And for the
solid sphere of same mass M, the moment of inertia M.I. about a vertical axis passing through
center is given by the relation:
As the radius R
of the disc is always greater than that of the sphere so,
the moment of inertia of disc is always greater that of the
sphere. Hence,
the M.I. about a vertical axis passing through the center
decreases as
a disc of metal recast in the form of a solid sphere.
110. Two metal
sphere have same mass and same radius. If one is hollow and the
other is solid, which will have greater M.I.?
As the moment
of inertia M.I. of a body
is given by relation I =
i.e. M.I. of a body not only depends upon the mass but also
depends upon the distribution of mass from the axis of
rotation. If two metal sphere have same mass and same radius
but one is hollow and the other is solid, then the hollow sphere will have greater
moment of inertia M.I. because most of
the mass is concentrated at large distance from the center.
111. There are two
circular discs of equal masses and thickness but made of
different materials. Which will have greater moment of inertia M.I. about its
central axis and why?
There are two
circular discs of equal masses and thickness but made of
different materials. As the moment of inertia M.I. of a body
is given by relation I =
i.e. M.I. of
a body not only depends upon the mass but also depends upon
the distribution of mass from the axis of rotation. The disc
made of less dense material will have large moment of inertia M.I because the
particles are at a greater distance from the axis rotation.
112. An object is
tied to a string and whirled in a circular path with uniform
speed. What will happen to the angular momentum of the object
when the string is suddenly cut?
According to
the law of conservation of angular momentum, "if no external
torque is applied on the system then the angular momentum of
that system remains constant". If an object is tied to a
string and whirled in a circular path with uniform speed,
the angular momentum of the system will still remain
conserved even after the string is cut as no any external
torque is applied on that system.
113. A wheel moving
down a perfectly frictionless inclined plane will undergo
slipping instead of rolling. Why?
A body rolls due to force of friction acting on it. If the
wheel is moving down a perfectly frictionless inclined plane,
it will be under the effect of its weight only. Since, weight
of the wheel acts along vertical through its center of mass,
the wheel will not rotated but will keep on slipping. Hence, a
wheel
moving down a perfectly frictionless inclined plane will
undergo slipping instead of rolling.
114. A circular
platform is rotating with a uniform angular velocity. What will
be the change in the motion of the platform if a person sits
person sits near the edge and then stars moving towards the
center of the platform?
Every
system will try to keep the angular momentum L conserved in
absence of external torque
(where I is moment of inertia &
w
be the
angular velocity). When the person sits near the edge of the platform, the value
of moment of inertia i.e. I will be increased. For the angular
momentum L to remain conserved, its
angular
velocity
w
has to be decreased and the platform will slow down.
When the person starts moving towards the center of the
platform, moment of inertia (I) will decrease while its
angular velocity
w
will
increase and the platform motion will be fast.
115. Why is ladder
more likely to slip when a person is high upon it than when he just
begins to climb?
When a person is high up, the moment of force tending to
rotate the ladder increases because of greater lever arm. When
he just begins to climb, the lever arm will be decreased and the
moment of force will be insufficient to cause slipping. Hence, ladder is more
likely to slip when a person is high upon it than when he
just begins to climb.
116. Some toys are made with their bases filled with clay or
lead shots. Why?
As the body
will be stable if its center of gravity i.e. C.G. lies
within the base of the body. When the base of some toys are
made heavy, there is a shifting of center of gravity to the
base of toys so that they are stable i.e. it causes the toys to remain in stable
equilibrium. Hence, some toys are made with their bases filled
with clay or lead shots.
117. A rope dancer holds an umbrella or pole to balance him. Why?
As the body will be stable if its center of gravity i.e.
C.G. lies within the base of the body. A ropedancer holds an
umbrella or pole to balance him in order to shift the center
of gravity i.e. C.G. within the base so that he or she can
enjoy stable equilibrium by gaining stability. Hence, a
ropedancer holds an umbrella or pole to balance him.
118. A man carrying a load on his back leans forward. Why? (HSEB
1996).
As the body will be stable if its center of gravity i.e.
C.G. lies within the base of the body.
A man carrying a load on his back leans forward so that the
vertical line through C.G. passes through the base. Further,
the position of C.G. will be lowered with respect to the
ground and makes him in stable equilibrium. Hence, a man
carrying a load on his back leans forward.
119. While coming down the hill, a person leans backwards. Why?
As the body will be stable if its center of gravity i.e.
C.G. lies within the base of the body.
While coming down the hill, a person leans backwards so that
the vertical line through the center of gravity i.e. C.G. lies within the base.
Further the height of C.G. will be decreased and he enjoys stable equilibrium state.
Hence, a person leans backwards while coming down the hill
in order to gain stability.
120. Trucks, cars and ships are made
with their base heavy. Why? (HSEB 1994)
As the body will be stable if its center of gravity i.e.
C.G. lies within the base of the body i.e. the base of that
body is to be made heavy in order to make that body stable.
The base of trucks, cars & ships are made heavy in order to
shift the position of center of mass C.M. within the base of
vehicles or ship in order that they will enjoy stable
equilibrium. Hence, trucks, cars and ships are made with
their base heavy.
