-
The sign of work done by a force on a body is important to understand. State carefully if the following quantities are positive or negative.
(i) Work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket.
(ii) Work done by gravitational force in the above case.
(iii) Work done by friction on a body sliding down an inclined plane.-
(iv) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity.
(v) Work done by the resistive force of air on a vibrating pendulum in bringing it to rest.
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A body of mass 2 kg initially at rest moves under the action of an applied horizontal force of 7N on a table with coefficient of kinetic friction = 0.1. Compute the
(i) work done by the applied force in 10s,
(ii) work done by the friction in 10 s,
(iii) work done by the net force on the body in 10 s, and
(iv) change in kinetic energy of the body in 10 s. Interpret your results.
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Given below (Pig. 6.46) are examples of
some potential energy functions in one dimension. The total energy of the particle
is indicated by a cross on the ordinate axis. In each case, specify the
regions, if any, in which the particle cannot be found
(a)
(b)
(c)
(d)
Fig. 6.46
for the given energy. Also, indicate the
minimum total energy the particle must have in each case. Think of simple
physical contexts for which these potential energy shapes are relevant.
-
The potential energy function for a
particle executing linear simple harmonic motion is given by
where k is the
force constant of the oscillator. For
the graph of
versus x is
shown in Fig. 6.47. Show that a particle of total energy 1 J moving under this
potential must "turn back" when it reaches
.
-
Answer the following
:
(a) The casing of a rocket in
flight burns up due to friction.
At whose expense is the heat
energy required for burning obtained ? The rocket or the atmosphere or both ?
[Delhi 12]
(b) Comets move around the sun
in highly elliptical orbits. The gravitational force on the comet due to the
sun is not normal to the comet's velocity in general. Yet the work done by the
gravitational force over every complete orbit of the comet is zero. Why
?
(c) An artificial satellite
orbiting the earth in very thin atmosphere loses its energy gradually due to
dissipation against atmospheric resistance, however small. Why then does its
speed increase progressively as it comes closer and closer to the earth
?
(d) In Fig. 6.48 (i) the man
walks 2 m carrying a mass of 15 kg on his hands. In Fig. 6.48 (ii), he walks
the same distance pulling the rope behind him. The rope goes over a pulley, and
a mass of 15kg hangs at its other end. In which case is the work done greater
?
Fig. 6.48
-
Underline the correct alternative:
(a) When a conservative force does positive work on a body, the potential energy of the body increases I decreases remains unaltered.
(b) Work done by a body against friction always results in a loss of its kinetic/potential energy.
(c) The rate of change of total momentum of a many-particle system is proportional to the external force/sum of the internal forces on the system.
(d) In an inelastic collision of two bodies, the quantities which do not change after the collision are the total kinetic energy/total linear momentum/total energy of the astern of two bodies.
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State if each of the following statements is true or false.
Give reasons for your answer.
(a) In an elastic collision of two bodies, the momentum and energy of each body is conserved.
(b) Total energy of a system is always conserved, no matter what internal and external forces on the body are present.
(c) Work done in the motion of a body over a closed loop is zero for every force in nature.
(d) In an inelastic collision, the final kinetic energy is always less than the initial kinetic energy of the system.
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Answer carefully, with reasons:
(a) In an elastic collision of two billiard balls, is the total kinetic energy conserved during the short time of collision of the balls (i.e., when they are in contact) ? [Delhi 12]
(b) Is the total linear momentum conserved during the short time of an elastic collision of two balls ?
(c) What are the answers to (a) and (b) for an inelastic collision ?
(d) If the potential energy of two billiard balls depends only on the separation distance between their centres, is the collision elastic or inelastic ? (Note, we are talking here of potential energy corresponding to the force during collision, not gravitational potential energy.)
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A body is initially at rest. It
undergoes one-dimensional motion with constant acceleration. The power
delivered to it at time t is proportional to
(i)
(ii)
(iii)
(iv)
-
A body is moving unidirectionally under
the influence of a source of constant power. Its displacement in time t is proportional
to
(i)
(ii)
(iii)
(iv)
-
A body constrained to move along the
Z-axis of co-ordinate system is subject to a constant ton
where
are unit
vectors along the
and
Z-axis of the system respectively. What is the war done by this force in moving
the body a distance of'4 m along the Z-axis ?
-
An electron and a proton are detected in
a cosmic ray experiment, the first with kinetic energy 10 keV, and the second with
100 keV. Which is faster, the electron or the proton ?
Obtain the ratio of their
speeds.
(Electron mass
proton mass
.
-
A rain drop of radius 2 mm falls from a height of 500 m above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height, it attains its maximum (terminal) speed and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey ?
What is the work done by the resistive force in the entire journey if its speed on reaching the ground is ?
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A molecule in a gas container hits a horizontal
wall with speed
and
angle 30° with the normal, and rebounds with the same speed. Is momentum
conserved in the collision ? Is the collision elastic or inelastic?
-
A pump on the ground floor of a building
can pump water to fill a tank of volume
in 15 min If
the tank is 40 m above the ground, and the efficiency of the pump is 30% i much
electric power is consumed by the pump ?
-
Two identical ball bearings in contact
with each other and resting on a frictionless table are hit head-on by another
ball bearing of the same mass moving initially with a speed v. If the collision
is elastic, which of the situations shown in Fig 6.50, is a possible result
after collision ?
Fig. 6.50
-
The bob A of a pendulum released from 30° to the vertical hits another bob B of the same mass at rest on a table as shown in Fig. 6.51. How high does the bob A rise after the collision ?
Neglect the size of the bobs and assume the collision to be elastic.
-
A trolley of mass 300 kg carrying a
sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track.
After a while, sand starts leaking out of a hole on the trolley's floor at the
rate
. What is the
speed of the trolley after the entire sand bag is empty ?
-
A trolley of mass 300 kg carrying a
sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track.
After a while, sand starts leaking out of a hole on the trolley's floor at the
rate
. What is the
speed of the trolley after the entire sand bag is empty ?
-
A particle of mass 0.5 kg travels in a
straight line with velocity
where
. What is the
work done by the net force during its displacement from
to
-
The blades of a windmill sweep out a
circle of area A.
(a) If the wind flows at a
velocity v perpendicular to the circle, what is the mass of the air passing
through it in time t ? (b) What is the kinetic energy of the air ? (c) Assume
that the windmill converts 25% of the wind's energy into electrical energy, and
that
and the density
of air is
.
What is the electrical power produced ?
-
A person trying to lose weight (dieter)
lifts a 10 kg mass 0.5 m, 1000 times. Assume that the potential energy lost each
time she lowers the mass is dissipated, (a) How much work does she do against
the gravitational force ?, (b) Fat supplies
of energy per
kilogram which is converted to mechanical energy with a 20% efficiency rate.
How much fat will the dieter use up ?
-
A large family uses 8 kW of power, (a)
Direct solar energy is incident on the horizontal surface at an average rate of
200 W per square meter. If 20% of this energy can be converted to useful
electrical energy, how large an area is needed to supply 8 kW ? (b) Compare
this area to that of the roof of a house constructed on a plot of size 20 m x
15 m with a permission to cover upto 70%
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A bullet of mass 0.012 kg and horizontal
speed
strikes a block
of wood of mass 0.4 kg and instantly comes to rest with respect to the block.
The block is suspended from the ceiling by means of thin wires. Calculate the
height to which the block rises. Also estimate the amount of heat produced in
the block. [Chandigarh 07]
-
Two inclined frictionless tracks, one
gradual and the other steep meet at A from where two stones are allowed to
slide down from rest, one on each track (Fig. 6.53). Will the stones reach the
bottom at the same time ? Will they reach there with the same speed ? Explain.
Given
and h = 10 m, what
are the speeds and times taken by the two stones ?
Fig. 6.53
-
A 1 kg block situated on a rough incline
is connected to a spring of spring constant 100 Nm~1 as shown in Fig. 6.54(a).
The block is released from rest with the spring in the unstretched position. The
block moves 10 cm down the incline before coming to rest. Find the coefficient
of friction between the block and the incline. Assume that spring has
negligible mass and the pulley is frictionless.
Fig. 6.54
-
A bolt of mass 0.3 kg falls from the
ceiling of an elevator moving down with a uniform speed of
. It hit the
floor of the elevator (length of the elevator 3 m) and does no rebound. What is
the heat produced by the impact ? Would you answer be different, if the
elevator were stationary ?
-
A trolley of mass 200 kg moves with a
uniform speed of 36 km I h on a frictionless track. A child of mass 20 kg runs on
the trolley from one end to the other (10 m away) with a speed of
relative to the
trolley in a direction opposite to the trolley's motion, and jumps out of the
trolley. What is the final speed of the trolley ? How much has the trolley
moved from the time the child begins to run ?
-
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Consider the decay of a free neutron at
rest:
Show that the two-body decay of
this type must necessarily give an electron of fixed energy and. therefore,
cannot account for the observed continuous energy distribution in the
-decay of
neutron or a nucleus (Fig. 6.56).
-
question_answer31)
An
electron and a proton are moving under the influence of mutual forces. In
calculating die change in the kinetic energy of die system during motion, one
ignores the magnetic force of one oil another. This is because,
(a)
the two magnetic forces are equal and opposite, so that produce no net effect.
(b)
the magnetic forces do no work oil each particle.
(c)
the magnetic forces do equal and opposite (but non-zero) work on each particle.
(d)
the magnetic forces are necessarily negligible.
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question_answer32)
A
proton is kept at rest. A position charged particle is released from rest at a
distance d in its field. Consider two experiments; one in which die charged
particle is also a proton and in another, a positron. In the same time t, the
work done oil the two moving charged particles is
(a)
same as the same force law is involved in die two experiments.
(b)
less for the case of a positron, as the positron moves away more rapidly and
the force oil it weakens.
(c)
more for die case of a positron, as die positron moves away a larger distance.
(d)
same as the work done by charged particle oil the stationary proton.
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question_answer33)
A
man squatting on the ground gets straight up and stand. The force of reaction
of ground on the man during the process is
(a)
constant and equal to mg in magnitude.
(b)
constant and greater than mg in magnitude.
(c)
variable but always greater than mg.
(d)
at first greater than mg, and later becomes equal to mg.
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question_answer34)
A
bicyclist comes to a skidding stop in 10 m. During this process, the force on
the bicycle due to the road is 200 N and is directly opposed to the motion. The
work done by the cycle on the road is
(a)
+ 2000 J (b) ? 200 J
(c)
zero (d) ? 20,000 J
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question_answer35)
A
body is falling freely under the action of gravity alone in vacuum. Which of
the following quantities remain constant during the fall?
(a)
Kinetic energy.
(b)
Potential energy.
(c)
Total mechanical energy.
(d)
Total linear momentum.
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question_answer36)
During
inelastic collision between two bodies, which of the following quantities
always remain conserved?
(a)
Total kinetic energy.
(b)
Total mechanical energy.
(c)
Total linear momentum.
(d)
Speed of each body.
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question_answer37)
Two
inclined frictionless tracks, one gradual and the other steep meet at A from
where two stones are allowed to slide down from rest, one on each track as
shown in Fig.
Which
of the following statement is correct?
(a)
Both the stones reach the bottom at the same time but not with the same speed.
(b)
Both the stones reach the bottom with the same speed and stone I reaches the
bottom earlier than stone II. (Fig.)
(c)
Both the stones reach the bottom wit: the same speed and stone II reaches the
bottom earlier than stone I.
(d) Both
the stones reach the bottom at different times and with different speeds
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question_answer38)
The
potential energy function for a particle executing linear SHM is given by \[V(x)=\,\frac{1}{2}\,k{{x}^{2}},\]
where k
is the force constant of the oscillator (Fig.) For k = 0.5 N/m, the
graph of \[V(x)\] versus
\[x\] is
shown in the figure. A particle of total energy E turns back when it reaches \[x=\pm
{{x}_{m}}\]. If V and K indicate the P.E. and K.E., respectively of the
particle at \[x=+{{x}_{m}},\] then which of the following correct?
(a) \[V=O,\] \[K=E\]
(b) \[V=E,\] \[K=O\]
(c) \[V<E,\] \[K=O\]
(d) \[V=O,\] \[K<E\]
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question_answer39)
Two
identical ball bearings in contact with each other and resting on a
frictionless table are hit head-on by another ball bearing of the same mass
moving initially with a speed V as shown in Fig.
If
the collision is elastic, which of the following (Fig.) is a possible result
after collision?
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question_answer40)
A
body of mass 0.5 kg travels in a straight line with velocity \[v=a\,{{x}^{3/2}}\]
where \[a=5\,\,{{m}^{-1/2}}\,{{s}^{-1}}\].
The work done by the net force during its displacement from \[x=0\] to \[x=2\,m\]
is
(a)
1.5 J (b) 50 J
(c)
10 J (d) 100 J
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question_answer41)
A
body is moving unidirectionally under the influence of a source of constant
power supplying energy. Which of the diagrams shown in Fig. correctly shows the
displacement-time curve for its motion?
(a)
(b) 
(c)
(d) 
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question_answer42)
Which
of the diagrams shown in Fig. most closely shows the variation in kinetic
energy of the earth as it moves once around the sun in its elliptical orbit?
(a)
(b) 
(c)
(d) 
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question_answer43)
Which
of the diagrams shown in Fig. represents variation of total mechanical energy
of a pendulum oscillating in air as function of time?
(a)
(b) 
(c)
(d) 
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question_answer44)
A
mass of 5 kg is moving along a circular path of radius 1 in. If the mass moves
with 300 revolutions per minute, its kinetic energy would be
(a)
\[250\,{{\pi }^{2}}\] (b) \[100\,{{\pi }^{2}}\]
(c)
\[5\,{{\pi }^{2}}\] (d) 0
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question_answer45)
A
raindrop falling from a height h above ground, attains a near terminal velocity
when it has fallen through a height (3/4)h. Which of the diagrams shown in Fig.
correctly shows the change in kinetic and potential energy of the drop during
its fall up to the ground?
(a)
(b) 
(c)
(d)
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question_answer46)
In
a shotput event an athlete throws the shotput of mass 10 kg with an initial
speed of \[1\,m\,{{s}^{-1}}\]at \[{{45}^{o}}\] from a height 1.5 in above ground.
Assuming air resistance to be negligible and acceleration due to gravity to be \[10m\,{{s}^{-2}}\],
the kinetic energy of the shotput when it just reaches the ground will be
(a)
2.5 J (b) 5.0 J
(c)
52.5 J (d) 155.0 J
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question_answer47)
Which
of the diagrams in Fig. correct] shows the change in kinetic energy of a iron
sphere falling freely in a lake having sufficient depth to impart it a terminal
velocity?
(a)
(b) 
(c)
(d) 
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question_answer48)
A
cricket ball of mass 150 g moving with a speed of 126 km/h hits at the middle
of the bat, held firmly at its position by the batsman. The ball moves straight
back to the bowler after hitting the bat. Assuming that collision between ball
and bat is completely elastic and the two remain in contact for 0.001s, the
force that the batsman had to apply to hold the bat firmly at its place would
be
(a)
10.5 N (b) 21 N
(c)
\[1.05\times {{10}^{4}}\,N\] (d) \[2.1\times {{10}^{4}}\,N\]
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question_answer49)
A
man, of mass m, standing at the bottom of the staircase, of height L climbs it
and stands at its top.
(a)
Work done by all forces on man is equal to the rise in potential energy mgL.
(b)
Work done by all forces on man is zero.
(c)
Work done by the gravitational force on man is mgL.
(d)
The reaction force from a step does not do work because the point of application
of the force does not move while the force exists.
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question_answer50)
A
bullet of mass m fired at \[{{30}^{o}}\] to the horizontal leaves the barrel of the
gun with a velocity \[\upsilon \]. The bullet hits a soft target at a height h
above the ground while it is moving downward and emerges out with half the
kinetic energy it had before hitting the target. Which of the following
statements are correct in respect of bullet after it emerges out of the target?
(a)
The velocity of the bullet will be reduced to half its initial value.
(b)
The velocity of the bullet will be more than half of its earlier velocity.
(c)
The bullet will continue to move along the same parabolic path.
The
bullet will move in a different parabolic path.
(e)
The bullet will fall vertically downward after hitting the target.
(f)
The internal energy of the particles of the target will increase.
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question_answer51)
Two
blocks \[{{M}_{1}}\] and
\[{{M}_{2}}\] having
equal mass are free to move on a horizontal frictionless surface. \[{{M}_{2}}\]is
attached to a massless spring as shown in Fig. Initially \[{{M}_{2}}\] is at rest and \[{{M}_{1}}\]
is moving
toward \[{{M}_{2}}\] with
speed v and collides head-on with \[{{M}_{2}}\].
(a) While spring is
fully compressed all the KE of \[{{M}_{1}}\] is stored as PE of spring.
(b) While spring is
fully compressed the system momentum is not conserved, through final momentum
is equal to initial momentum.
(c) If spring is
massless, the final state of the \[{{M}_{1}}\] is state of rest.
(d) If the surface
on which blocks are moving, has friction, then collision cannot be elastic.
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question_answer52)
A
rough inclined plane is placed on a cart moving with a constant velocity \[u\]
on horizontal
ground. A block of mass M rests on the incline. Is any work done by force of
friction between the block and incline? Is there then a dissipation of energy?
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question_answer53)
Why
is electrical power required at all when die elevator is descending? Why should
there be a limit on the number of passengers in this case?
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question_answer54)
A body is being
raised to a height h from the surface of earth. What is the sign of work done
by
(a)
applied force
(b)
gravitational force
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question_answer55)
Calculate
the work done by a car against gravity in moving along a straight horizontal
road. The mass of the car is 400 kg and the distance moved is 2 m.
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question_answer56)
A
body falls towards earth in air. Will its total mechanical energy be conserved during
the fall? Justify.
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question_answer57)
A
body is moved along a closed loop. Is the work done in moving the body
necessarily zero? If not, state the condition under which work done over a
closed path is always zero.
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question_answer58)
In an elastic
collision of two billiard balls, which of the following quantities remain
conserved during the short time of collision of the balls (i.e., when they are
in contact).
(a)
Kinetic energy.
(b)
Total linear momentum?
Give
reason for your answer in each case.
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question_answer59)
Calculate
the power of a crane in watts, which lifts a mass of 100 kg to a height of 10
in in 20 s.
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question_answer60)
The
average work done by a human heart while it beats once is 0.5 J. Calculate the
power used by heart if it beats 72 times in a minute.
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question_answer61)
Give
example of a situation in which an applied force does not result in a change in
kinetic energy.
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question_answer62)
Two
bodies of unequal mass are moving in the same direction with equal kinetic
energy. The two bodies are brought to rest by applying retarding force of same
magnitude.' How would the distance moved by them before coming to rest compare?
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question_answer63)
A bob of mass m
suspended by a light string of length is whirled into a vertical circle as
shown in Fig. What will be the trajectory of the particle if the string is cut
at
(a) Point B ? (b)
Point C ?
(c) Point X ?
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question_answer64)
A
graph of potential energy \[V(x)\] verses \[x\] is shown in Fig. A particle of
energy \[{{E}_{0}}\] is
executing motion in it. Draw graph of velocity and kinetic energy versus x for
one complete cycle AFA.
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question_answer65)
A ball of mass m,
moving with a speed \[2\,{{\upsilon }_{0}}\], collides inelastically \[(e>0)\]
with an
identical ball at rest. Show that
(a)
For head-on collision, both the balls move forward.
(b)
For a general collision, the angle between the two velocities of scattered
balls is less than \[{{90}^{o}}\].
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question_answer66)
Consider
a one-dimensional motion of a particle with total energy E. There are four
regions A, B, C and D in which the relation between potential energy V, kinetic
energy (K) and total energy E is as given below:
Region
A : V > E
Region
B : V < E
Region
C : K > E
Region
D : V > K
State
with reason in, each case whether a particle can be found in the given region
or not.
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question_answer67)
The
bob A of a pendulum released from horizontal to the vertical hits another bob B
of the same mass at rest on a table as shown in Fig.
If
the length of the pendulum is 1m, calculate
(a)
the height to which bob A will rise after collision.
(b)
the speed with which bob B starts moving. Neglect die size of the bobs and
assume die collision to be elastic.
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question_answer68)
A raindrop of mass
1.00 g falling from a height of 1 km hits the ground with a speed of \[50\,\,m\,{{s}^{-1}}\].
Calculate
(a)
the loss of P.E. of the drop.
(b)
the gain in K.E. of the drop.
(c)
Is the gain in K.E. equal to loss of P.E.? It not why.
Take
\[g=10\,m{{s}^{-2}}\]
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question_answer69)
Two
pendulums with identical bobs and lengths are suspended from a common support
such that in rest position the two bobs are in contact (Fig.). One of the bobs
is released after being displaced by 10' so that it collides elastically
head-on with the other bob.
(a)
Describe the motion of two bobs.
(b)
Draw a graph showing variation in energy of either pendulum with time, for \[0\,\le
\,t\le \,2T,\]where T is the period of each pendulum.
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question_answer70)
Suppose
the average mass of raindrops is \[3.0\times {{10}^{-5}}\,kg\]and their average
terminal velocity \[9\,m\,{{s}^{-1}}\]. Calculate the energy transferred by
rain to each square metre of the surface at a place which receives 100 cm of
rain in a year.
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question_answer71)
An engine is
attached to a wagon through a shock absorber of length 1.5 m. The system with a
total mass of 50,000 kg is moving with a speed of \[36\,km\,{{h}^{-1}}\] when
the brakes are applied to bring it to rest. In the process of the system being
brought to rest, the spring of the shock absorber gets compressed by 1.0 m. If
90% of energy of the wagon is lost due to friction, calculate the spring
constant.
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question_answer72)
An
adult weighing 600 N raises the centre of gravity of his body by 0.25 m while
taking each step of 1 m length in jogging. If he jogs for 6 km, calculate the
energy utilised by him in jogging assuming that there is no energy loss due to
friction of ground and air. Assuming that the body of the adult is capable of
converting 10% of energy intake in the form of food, calculate the energy
equivalents of food that would be required to compensate energy utilised for
jogging.
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question_answer73)
On complete
combustion a litre of petrol gives off heat equivalent to \[3\times
{{10}^{7}}\,J\] . In a test drive, a car weighing 1200 kg including the mass of
driver, runs 15 kin per litre while moving with a uniform speed on a straight
track. Assuming that friction offered by the road surface and air to be
uniform, calculate the force of friction acting on the car during the test
drive, if the efficiency of the car engine were 0.5.
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question_answer74)
A
block of mass 1 kg is pushed up a surface inclined to horizontal at an angle of
\[{{30}^{o}}\] by
a force of 10 N parallel to the inclined surface (Fig.).The coefficient of
friction between block and the incline is 0.1. If the block is pushed up by 10
m along the incline, calculate
(a)
work done against gravity
(b)
work done against force of friction
(c)
increase in potential energy
(d)
increase in kinetic energy
(e)
work done by applied force.
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question_answer75)
A
curved surface is shown in Fig. The portion BCD is free of friction. There are three
spherical balls of identical radii and masses. Balls are released from rest one
by one from A which is at a slightly greater height than C.
With
the surface AB, ball 1 has large enough friction to cause rolling, down without
slipping; ball 2 has a small friction and ball 3 has a negligible friction.
(a)
For which balls is total mechanical energy conserved?
(b)
Which ball (s) can reach D?
(c)
For balls which do not reach D, which of the balls call reach back A?
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question_answer76)
A rocket
accelerates straight up by ejecting gas downwards. Ina small time interval \[\Delta
t,\] it ejects a gas of mass \[\Delta m\] at a relative speed u. Calculate KE of the
entire system at \[t+\Delta t\] and t and show that the device that
ejects gas does work \[=(1/2)\,\Delta m{{u}^{2}}\] in this time interval
(neglect gravity).
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question_answer77)
Two identical steel
cubes (masses 50 g, side 1 cm) collide head-on face to face with a speed of 10
cm/s each. Find the maximum compression of each. Young?s modulus for steel \[=Y=2\times
{{10}^{11}}N/{{m}^{2}}\].
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question_answer78)
A
balloon filled with helium rises against gravity increasing its potential
energy. The speed of the balloon also increases as it rises. How do you
reconcile this with the law of conservation of mechanical energy? You can
neglect viscous drag of air and assume that density of air is constant.
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