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Case study
1. In everyday life, the term work is used to refer to any form of activity that requires the
exertion of mental or muscular efforts. In physics, work is said to be done by a force
or against the direction of the force, when the point of application of the force moves
towards or against the direction of the force. If no displacement takes place, no work
is said to be done.
i. A box is pushed through 4.0 m across a floor offering 100 N resistance. How much
work is done by the applied force?
a. 100J b. 200 J c. 300 J d. 400 J
ii. What is work done in holding a 15 kg suitcase while waiting for 15 minutes?
a. 22.5 J b. 225 J c. zero d. 150 J
iii. Frictional forces are:
a. conservative forces b. non- conservative forces
c. buoyant force d. none of these
iv. When the body moves in circular motion, net 'work' done is:
a. positive b. negative c. zero d. none of these
In physics, we come across many examples of collisions. The molecules of a gas
collide with one another and with the container. The collisions of a neutron with an
atom is well known. In a nuclear reactor, fast neutrons produced in the fission of
uranium atom have to be slowed down. They are, therefore, made to collide with
hydrogen atom. The term collision does not necessarily mean that a particle or a body
must actually strike another. In fact, two particles may not even touch each other and
yet they are said to collide if one particle influences the motion of the other. When
two bodies collide, each body exerts an equal and opposite force on the other. The
fundamental conservation law of physics is used to determine the velocities of the
bodies after the collision. Collision may be elastic or inelastic. Thus, a collision may
be defined as an event in which two or more bodies exert relatively strong forces on
each other for a relatively short time. The forces that the bodies exert on each other
are internal to the system. Almost all the knowledge about the sub-atomic particles
such as electrons, protons, neutrons, muons, quarks, etc. is obtained from the
experiments involving collisions. There are certain collisions called nuclear reactions
in which new particles are formed. For example, when a slow neutron collides with a
U235 nucleus, new nuclei barium-141 and Kr92 are formed. This collision is called
nuclear fission. In nuclear fusion, two nuclei deuterium and tritium collide (or fuse) to
form a helium nucleus with the emission of a neutron.
i. Which one of the following collisions is not elastic?
(A) A hard steel ball dropped on a hard concrete floor and rebounding to its original
height. (B) Two balls moving in the same direction collide and stick to each other
(C) Collision between molecules of an ideal gas.
(D) Collisions of fast neutrons with hydrogen atoms in a fission reactor.
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ii. Which one of the following statements is true about inelastic collision?
(A)The total kinetic energy of the particles after collision is equal to that before
collision.
(B) The total kinetic energy of the particle after collision is less than that before
collision.
(C) The total momentum of the particles after collision is less than that before
collision.
(D) Kinetic energy and momentum are both conserved in the collision.
III. In elastic collision
(A) Only energy is conserved.
(B) Only momentum is conserved.
(C) Neither energy nor momentum is conserved.
(D) Both energy and momentum are conserved.
3. Most of the substanceβs solids, liquid, and gases expand on heating and contract on
cooling. Their thermal expansions and contractions are usually small and are not
noticeable. However, these expansions and contractions are important in our daily
life. The expansion of solids may damage the bridges, railway tracks, and roads as
they are constantly subjected to temperature changes.
i) Water has maximum density at
(a) 0
0
C
(b) 100
0
C
(c) 4
0
C
(d) 32
0
C
(ii) Ratio of linear expansion coefficient, areal expansion coefficient and volume
expansion coefficient is
(a) 1: 2: 3
(b) 3: 2: 1
(c) 4: 3: 2
(d) none of these
(iii) As the temperature is increased, the time period of a pendulum
(a) increases as its effective length increases even though its centre of mass still
remains at the centre of the bob.
(b) decreases as its effective length increases even though its centre of mass still
remains at the centre of the bob.
(c) increases as its effective length increases due to shifting of centre of mass below
the centre of the bob.
(d) decreases as its effective length remains same but the centre of mass shifts above
the centre of the bob
(iv) i) When a bimetallic strip is heated
(a) Does not bend at all
(b) Gets twisted in the form of a helix
(c) Bends in the form of an arc with the more expandable metal outside
(d) Bends in the form of an arc with the more expandable metal inside
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4.The centre of mass of a body is a point at which the entire mass of the body is supposed to be
concentrated. The position vector ξΊ of C.O.M. of the system of two particles of masses m1 and m2
with position vectors ξ΄ ο and ξ΄ ο is given by ξΊ = π¦ο ξ΄ ο +
π¦οξ΄ ο π¦ο+π¦ο for isolated system, where no external force is acting,
Vcm = constant Under no circumstances, the velocity of the C.O.M. of an isolated system can
undergo a change. With the help of above comprehension, choose the most appropriate alternative
for each of the following questions:
1. Two bodies of masses 1kg and 2kg are located at (1,2) and (-1,3) respectively. The co-ordinates of
C.O.M. are
(a) (-1, 3) (c) (β ο/ π, π /π)
(b) (1, 2) (d) (ο/ π, β π /π)
2.. A bomb dropped from an aeroplane in level flight explodes in the middle. The centre of mass of
the fragments
(a) is at rest (b) Moves vertically downwards
(c) Moves vertically upwards (d) continues to follow the same parabolic path which it would have
followed if there was no explosion.
3.Where is the position of the centre of mass of a uniform triangular lamina?
4. Where is the position of the centre of mass of a rectangular lamina?
Potential energy of a body is the energy possessed by the body by virtue of its position. P.E.=m g h
where the symbols have their usual meaning. Kinetic energy of a body is the energy possessed by the
body by virtue of its velocity. K.E. = ο/ ο mv
2
Energy can neither be created nor be destroyed.
However, energy can be changed from one form to the other, such that energy appearing in one form
is equal to the energy disappearing in other form. With the help of above comprehension, choose the
most appropriate alternative for each of the following questions:
i)A body of mass 10kg is travelling with uniform speed of 5m/s. Its kinetic energy is
a)25J b)125J c)1250J d)1000J
ii)A body of mass 10 Kg moving at a hight of 2m, with uniform speed of 2m/s. Its total energy is
a)316J b)216J c)116J d)392J
iii)A body of mass 20 kg is dropped from a height of 2m. IF g is taken to be equal to 10m/s, the
kinetic energy of the body, just before striking the ground will be
a)400J b)50J c)100J d)300J
iv)A body of mass 20 kg is initially at a height of 3m above the ground. It is lifted to a height of 2m
from that position. Its increase in potential energy is
a)100J b)392J c)400J d)-100J
6.Moment of inertia of a body about a given axis is the rotational inertia of the body about that axis.
It is represented by I= MK
2
, where M is mass of body and K is radius of gyration of the body about
that axis. It is a scalar quantity, which is measured in kgm
2
. When a body rotates about a given axis,
and the axis of rotation also moves, then total K.E. of body =K.E. of translation + K.E. of rotation E = ο
/ο mv
2
+ ο/ ο IΟ
2
with the help of above comprehension, choose the most appropriate alternative
for each of the following questions:
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1. Moment of inertia of a body depends on
(i) mass of body (ii) size and shape of body
(iii) axis of rotation of body (iv) all the above
2.On which of the following factor does the moment of inertia of an object not depend up on
i)Axis of rotation ii) Mass of an object iii) Angular velocity iv) distribution of mass
3.When does the moment of inertia of a body come in to picture?
i)When the motion is linear ii) When the motion is along a curved path iii) when the motion is
rotational iv) none of the above
4.. A circular disc and a circular ring of same mass and same diameter have _____________________
(a) same moment of inertia (b) unequal moments of inertia
(c) cannot say (d) sometimes equal sometimes not
7. According to Newtonβs second law of motion, F = m. a, where F is the force required to produce an
acceleration a in a body of mass m. If a= 0 then F = 0, i. e, no external force is required to move a
body uniformly along a straight line. If a force F acts on a body for t seconds, the effect of the force is
given by impulse = F x t = change in linear momentum of the body. With the help of above
comprehension, choose the most appropriate alternative for each of the following questions:
1. An impulsive force of 100N acts on a body for 1s. What is the change in its linear momentum?
(a) 10Ns (c) 1000Ns (b) 100Ns (d) 1Ns
2.. A cricket ball of mass 150g is moving with a velocity of 12m/s and is hit by a bat so that the ball is
turned back with a velocity of 20m/s. If duration of contact between the ball and the bat is 0.01 sec.
The impulse of the force is
(a) 7.4Ns (c) 1.2Ns (b) 4.8Ns (d) 4.7Ns
3.A cricketer catches a ball of mass 150g in 0.1s moving with a speed of 20m/s. what is the force
here?
a) 30 N b)50N c)35N d)100N
8.
The contact angle is the angle, conventionally measured through the liquid, where a liquid vapour
interface meets a solid surface. It quantify the wettability of a solid surface by a liquid .the contact
angle depends up on the medium above the free surface of the liquid, and the nature
of the liquid and solid in contact. It changes with surface tension and hence with temperature and
purity of the liquid.
i)If the surface of the liquid is plane, then the angle of contact of the liquid with the walls of the
container isβ¦..
a) Acute angle b) obtuse angle c)90 d)0
ii)A liquid wets a solid completely. The meniscus of the liquid in a sufficiently long tube isβ¦
a) Flat b) Concave c) convex d) cylindrical
iii) the liquid meniscus in the capillary tube will be convex if the angle of contact is
a) Greater than 90 b) Less than 90 c) equal to 90 d)0
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iv) A mercury drop does not spread on a glass plate because the angle of contact between glass and
mercury is
a) Acute b) obtuse c)0 d) 90
v) the angle of contact between glass and mercury is
a) 0 b) 30 c)90 d)135