Oscillations- 2 Practice Questions - DPP for NEET

 Page 1


DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONL Y ONE choice is correct.
Q.1 A particle of mass m is
attached to three identical
springs A, B and C each of
force constant k as shown
in figure.
A
B
C
O
m
90°
If the particle of mass m
is pushed slightly against
the spring A and released
then the time period of
oscillations is
(a)
2
2
m
k
p (b) 2
2
m
k
p (c) 2
m
k
p (d) 2
3
m
k
p
Q.2 Three masses 700g, 500g, and 400g are suspended at the
end of a spring as shown and are in equilibrium.
When the 700g mass is removed, the system oscillates
with a period of 3 seconds, when the 500 gm mass is also
removed, it will oscillate with a period of
(a) 1 s
(b) 2 s
(c) 3 s
700gm
500gm
400gm
(d)
12
5
s
Page 2


DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONL Y ONE choice is correct.
Q.1 A particle of mass m is
attached to three identical
springs A, B and C each of
force constant k as shown
in figure.
A
B
C
O
m
90°
If the particle of mass m
is pushed slightly against
the spring A and released
then the time period of
oscillations is
(a)
2
2
m
k
p (b) 2
2
m
k
p (c) 2
m
k
p (d) 2
3
m
k
p
Q.2 Three masses 700g, 500g, and 400g are suspended at the
end of a spring as shown and are in equilibrium.
When the 700g mass is removed, the system oscillates
with a period of 3 seconds, when the 500 gm mass is also
removed, it will oscillate with a period of
(a) 1 s
(b) 2 s
(c) 3 s
700gm
500gm
400gm
(d)
12
5
s
2
DPP/ P 28
Q.3 The bob of a simple pendulum is displaced from its
equilibrium position O to a position Q which is at height h
above O and the bob is then released.
Assuming the mass of the bob to be m and time period of
oscillations to be 2.0 sec, the tension in the string when
the bob passes through O is
(a) ( 2) m g gh +p
(b)
2
() m g gh +p
(c)
2
2
m g gh
æö
p
ç÷
+
ç÷
èø
h
Q
O (d)
2
3
m g gh
æö
p
ç÷
+
ç÷
èø
Q.4 A spring of force constant k is cut into two pieces such
that one piece is double the length of the other. Then the
long piece will have a force constant of
(a) (2 / 3)k (b) (3 / 2)k (c)3k (d)6k
Q.5 A pendulum suspended from the ceiling of a train has a
period T, when the train is at rest. When the train is
accelerating with a uniform acceleration a, the period of
oscillation will
(a) increase (b) decrease
(c) remain unaffected (d) become infinite
Q.6 A simple pendulum is set up in a trolley which moves to the
right with an acceleration a on a horizontal plane. Then the
thread of the pendulum in the mean position makes an angle
q with the vertical is
(a)
1
tan
a
g
-
 in the forward direction
(b)
1
tan
a
g
-
 in the backward direction
(c)
1
tan
g
a
-
 in the backward direction
(d)
1
tan
g
a
-
 in the forward direction
Q.7 The time period of a second’s pendulum is 2 sec. The
spherical bob which is empty from inside has a mass of 50
gm. This is now replaced by another solid bob of same
radius but having different mass of 100 gm. The new time
period will be
(a) 4 sec (b) 1 sec (c) 2 sec (d) 8 sec
Q.8 The length of a simple pendulum is increased by 1%. Its
time period will
(a) Increase by 1% (b) Increase by 0.5%
(c) Decrease by 0.5% (d) Increase by 2%
Q.9 The bob of a pendulum of length l is pulled aside from its
equilibrium position through an angle q and then released.
The bob will then pass through its equilibrium position with
a speed v, where v equals
(a) 2 (1 sin) gl -q (b) 2 (1 cos) gl+q
(c) 2 (1 cos) gl-q (d) 2 (1 sin) gl +q
Q.10 A simple pendulum is executing simple harmonic motion
with a time period T. If the length of the pendulum is
increased by 21%, the percentage increase in the time
period of the pendulum of is
(a) 10% (b) 21% (c) 30% (d) 50%
Q.11 A chimpanzee swinging on a swing in a sitting position,
stands up suddenly, the time period will
(a) Become infinite (b) Remain same
(c) Increase (d) Decrease
Q.12 A simple pendulum consisting of a ball of mass m tied to a
thread of length l is made to swing on a circular arc of angle q
in a vertical plane. At the end of this arc, another ball of mass
m is placed at rest. The momentum transferred to this ball at
rest by the swinging ball is
(a) Zero (b)
g
m
l
q (c)
ml
lg
q
(d) 2
ml
lg
p
Q.13The time period of a simple pendulum of length L as
measured in an elevator descending with acceleration g / 3
is
(a)
3
2
L
g
p (b)
3L
g
æö
p
ç÷
èø
(c)
3
2
2
L
g
æö
p
ç÷
èø
(d)
2
2
3
L
g
p
Page 3


DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONL Y ONE choice is correct.
Q.1 A particle of mass m is
attached to three identical
springs A, B and C each of
force constant k as shown
in figure.
A
B
C
O
m
90°
If the particle of mass m
is pushed slightly against
the spring A and released
then the time period of
oscillations is
(a)
2
2
m
k
p (b) 2
2
m
k
p (c) 2
m
k
p (d) 2
3
m
k
p
Q.2 Three masses 700g, 500g, and 400g are suspended at the
end of a spring as shown and are in equilibrium.
When the 700g mass is removed, the system oscillates
with a period of 3 seconds, when the 500 gm mass is also
removed, it will oscillate with a period of
(a) 1 s
(b) 2 s
(c) 3 s
700gm
500gm
400gm
(d)
12
5
s
2
DPP/ P 28
Q.3 The bob of a simple pendulum is displaced from its
equilibrium position O to a position Q which is at height h
above O and the bob is then released.
Assuming the mass of the bob to be m and time period of
oscillations to be 2.0 sec, the tension in the string when
the bob passes through O is
(a) ( 2) m g gh +p
(b)
2
() m g gh +p
(c)
2
2
m g gh
æö
p
ç÷
+
ç÷
èø
h
Q
O (d)
2
3
m g gh
æö
p
ç÷
+
ç÷
èø
Q.4 A spring of force constant k is cut into two pieces such
that one piece is double the length of the other. Then the
long piece will have a force constant of
(a) (2 / 3)k (b) (3 / 2)k (c)3k (d)6k
Q.5 A pendulum suspended from the ceiling of a train has a
period T, when the train is at rest. When the train is
accelerating with a uniform acceleration a, the period of
oscillation will
(a) increase (b) decrease
(c) remain unaffected (d) become infinite
Q.6 A simple pendulum is set up in a trolley which moves to the
right with an acceleration a on a horizontal plane. Then the
thread of the pendulum in the mean position makes an angle
q with the vertical is
(a)
1
tan
a
g
-
 in the forward direction
(b)
1
tan
a
g
-
 in the backward direction
(c)
1
tan
g
a
-
 in the backward direction
(d)
1
tan
g
a
-
 in the forward direction
Q.7 The time period of a second’s pendulum is 2 sec. The
spherical bob which is empty from inside has a mass of 50
gm. This is now replaced by another solid bob of same
radius but having different mass of 100 gm. The new time
period will be
(a) 4 sec (b) 1 sec (c) 2 sec (d) 8 sec
Q.8 The length of a simple pendulum is increased by 1%. Its
time period will
(a) Increase by 1% (b) Increase by 0.5%
(c) Decrease by 0.5% (d) Increase by 2%
Q.9 The bob of a pendulum of length l is pulled aside from its
equilibrium position through an angle q and then released.
The bob will then pass through its equilibrium position with
a speed v, where v equals
(a) 2 (1 sin) gl -q (b) 2 (1 cos) gl+q
(c) 2 (1 cos) gl-q (d) 2 (1 sin) gl +q
Q.10 A simple pendulum is executing simple harmonic motion
with a time period T. If the length of the pendulum is
increased by 21%, the percentage increase in the time
period of the pendulum of is
(a) 10% (b) 21% (c) 30% (d) 50%
Q.11 A chimpanzee swinging on a swing in a sitting position,
stands up suddenly, the time period will
(a) Become infinite (b) Remain same
(c) Increase (d) Decrease
Q.12 A simple pendulum consisting of a ball of mass m tied to a
thread of length l is made to swing on a circular arc of angle q
in a vertical plane. At the end of this arc, another ball of mass
m is placed at rest. The momentum transferred to this ball at
rest by the swinging ball is
(a) Zero (b)
g
m
l
q (c)
ml
lg
q
(d) 2
ml
lg
p
Q.13The time period of a simple pendulum of length L as
measured in an elevator descending with acceleration g / 3
is
(a)
3
2
L
g
p (b)
3L
g
æö
p
ç÷
èø
(c)
3
2
2
L
g
æö
p
ç÷
èø
(d)
2
2
3
L
g
p
DPP/ P 28
3
Q.14A mass m is suspended from the two coupled springs
connected in series. The force constant for springs are k
1
and k
2
. The time period of the suspended mass will be
(a)
12
2
æö
=p
ç÷
+
èø
m
T
kk
(b)
12
2
æö
=p
ç÷
+
èø
m
T
kk
(c)
12
12
()
2
æö +
=p
ç÷
èø
mkk
T
kk
(d)
12
12
2
æö
=p
ç÷
+
èø
mkk
T
kk
Q.15 A spring having a spring constant k is loaded with a mass
m. The spring is cut into two equal parts and one of these is
loaded again with the same mass. The new spring constant is
(a) k / 2 (b) k (c)2k (d) k
2
Q.16 A mass m = 100 gm is attached at the end of a light spring
which oscillates on a frictionless horizontal table with an
amplitude equal to 0.16 metre and time period equal to 2
sec. Initially the mass is released from rest at t = 0 and
displacement x = –0.16 metre. The expression for the
displacement of mass at any time t is
(a) 0.16cos( ) xt =p (b) 0.16cos( ) xt =-p
(c) 0.16sin( ) xt = p +p (d) 0.16sin( ) xt = - p +p
Q.17 Two masses m
1
 and m
2
 are suspended together by a massless
spring of constant k. When the masses are in equilibrium,
m
1
 is removed without disturbing the system. The amplitude
of oscillations is
(a) 
1
mg
k
(b)
2
mg
k
(c) 
12
() + m mg
k
1
m
2
m
(d)
12
() - m mg
k
Q.18 The composition of two simple harmonic motions of equal
periods at right angle to each other and with a phase
difference of p results in the displacement of the particle
along
(a) Straight line (b) Circle
(c) Ellipse (d) Figure of 8
Q.19A particle with restoring force proportional to
displacement and resisting force proportional to velocity
is subjected to a force F sin wt. If the amplitude of the
particle is maximum for w = w
1
 and the energy of the particle
is maximum for w = w
2
, then (where w
0 
natural frequency
of oscillation of particle)
(a)
10
w =w and 
20
w ¹w (b)
10
w =w and 
20
w =w
(c)
10
w ¹w and 
20
w =w (d)
10
w ¹w and 
20
w ¹w
Q.20 Amplitude of a wave is represented by 
c
A
a bc
=
+-
Then resonance will occur when
(a) b = – c/2 (b) b = 0 & a =  c
(c) b = – a/2 (d) None
DIRECTIONS (Q.21-Q.23) : In the following questions,
more than one of the answers  given are correct. Select the
correct answers and mark it according to the following
codes:
Codes :
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.21Two blocks A and B each of mass m are connected by a
massless spring of natural length L and spring constant k.
The blocks are initially resting on a smooth horizontal floor
with the spring at its natural length. A third identical block
C also of mass m moves on the floor with a speed v along
the line joining A and B and collides with A. Then
(1) The kinetic energy of the A – B system at maximum
compression of the spring is mv
2
/4
(2) The maximum compression of the spring is v m / 2k
(3) The kinetic energy of the A-B system at maximum
compression of the spring is zero
(4) The maximum compression of the spring is v m/k
Q.22A simple pendulum of length L and mass (bob) M is
oscillating in a plane about a vertical line between angular
limits – f and + f. For an angular displacement ( ) ?? , <f
the tension in the string and the velocity of the bob are T
and v respectively . The following relations hold good under
the above conditions
(1)
2
Mv
T Mgcos?
L
-=
(2) Tcos? Mg =
(3)   The magnitude of the tangential acceleration of the bob
T
a gsin? =
(4) T = Mg cos q
Page 4


DIRECTIONS (Q.1-Q.20) : There are 20 multiple choice
questions. Each question has 4 choices (a), (b), (c) and (d), out
of which ONL Y ONE choice is correct.
Q.1 A particle of mass m is
attached to three identical
springs A, B and C each of
force constant k as shown
in figure.
A
B
C
O
m
90°
If the particle of mass m
is pushed slightly against
the spring A and released
then the time period of
oscillations is
(a)
2
2
m
k
p (b) 2
2
m
k
p (c) 2
m
k
p (d) 2
3
m
k
p
Q.2 Three masses 700g, 500g, and 400g are suspended at the
end of a spring as shown and are in equilibrium.
When the 700g mass is removed, the system oscillates
with a period of 3 seconds, when the 500 gm mass is also
removed, it will oscillate with a period of
(a) 1 s
(b) 2 s
(c) 3 s
700gm
500gm
400gm
(d)
12
5
s
2
DPP/ P 28
Q.3 The bob of a simple pendulum is displaced from its
equilibrium position O to a position Q which is at height h
above O and the bob is then released.
Assuming the mass of the bob to be m and time period of
oscillations to be 2.0 sec, the tension in the string when
the bob passes through O is
(a) ( 2) m g gh +p
(b)
2
() m g gh +p
(c)
2
2
m g gh
æö
p
ç÷
+
ç÷
èø
h
Q
O (d)
2
3
m g gh
æö
p
ç÷
+
ç÷
èø
Q.4 A spring of force constant k is cut into two pieces such
that one piece is double the length of the other. Then the
long piece will have a force constant of
(a) (2 / 3)k (b) (3 / 2)k (c)3k (d)6k
Q.5 A pendulum suspended from the ceiling of a train has a
period T, when the train is at rest. When the train is
accelerating with a uniform acceleration a, the period of
oscillation will
(a) increase (b) decrease
(c) remain unaffected (d) become infinite
Q.6 A simple pendulum is set up in a trolley which moves to the
right with an acceleration a on a horizontal plane. Then the
thread of the pendulum in the mean position makes an angle
q with the vertical is
(a)
1
tan
a
g
-
 in the forward direction
(b)
1
tan
a
g
-
 in the backward direction
(c)
1
tan
g
a
-
 in the backward direction
(d)
1
tan
g
a
-
 in the forward direction
Q.7 The time period of a second’s pendulum is 2 sec. The
spherical bob which is empty from inside has a mass of 50
gm. This is now replaced by another solid bob of same
radius but having different mass of 100 gm. The new time
period will be
(a) 4 sec (b) 1 sec (c) 2 sec (d) 8 sec
Q.8 The length of a simple pendulum is increased by 1%. Its
time period will
(a) Increase by 1% (b) Increase by 0.5%
(c) Decrease by 0.5% (d) Increase by 2%
Q.9 The bob of a pendulum of length l is pulled aside from its
equilibrium position through an angle q and then released.
The bob will then pass through its equilibrium position with
a speed v, where v equals
(a) 2 (1 sin) gl -q (b) 2 (1 cos) gl+q
(c) 2 (1 cos) gl-q (d) 2 (1 sin) gl +q
Q.10 A simple pendulum is executing simple harmonic motion
with a time period T. If the length of the pendulum is
increased by 21%, the percentage increase in the time
period of the pendulum of is
(a) 10% (b) 21% (c) 30% (d) 50%
Q.11 A chimpanzee swinging on a swing in a sitting position,
stands up suddenly, the time period will
(a) Become infinite (b) Remain same
(c) Increase (d) Decrease
Q.12 A simple pendulum consisting of a ball of mass m tied to a
thread of length l is made to swing on a circular arc of angle q
in a vertical plane. At the end of this arc, another ball of mass
m is placed at rest. The momentum transferred to this ball at
rest by the swinging ball is
(a) Zero (b)
g
m
l
q (c)
ml
lg
q
(d) 2
ml
lg
p
Q.13The time period of a simple pendulum of length L as
measured in an elevator descending with acceleration g / 3
is
(a)
3
2
L
g
p (b)
3L
g
æö
p
ç÷
èø
(c)
3
2
2
L
g
æö
p
ç÷
èø
(d)
2
2
3
L
g
p
DPP/ P 28
3
Q.14A mass m is suspended from the two coupled springs
connected in series. The force constant for springs are k
1
and k
2
. The time period of the suspended mass will be
(a)
12
2
æö
=p
ç÷
+
èø
m
T
kk
(b)
12
2
æö
=p
ç÷
+
èø
m
T
kk
(c)
12
12
()
2
æö +
=p
ç÷
èø
mkk
T
kk
(d)
12
12
2
æö
=p
ç÷
+
èø
mkk
T
kk
Q.15 A spring having a spring constant k is loaded with a mass
m. The spring is cut into two equal parts and one of these is
loaded again with the same mass. The new spring constant is
(a) k / 2 (b) k (c)2k (d) k
2
Q.16 A mass m = 100 gm is attached at the end of a light spring
which oscillates on a frictionless horizontal table with an
amplitude equal to 0.16 metre and time period equal to 2
sec. Initially the mass is released from rest at t = 0 and
displacement x = –0.16 metre. The expression for the
displacement of mass at any time t is
(a) 0.16cos( ) xt =p (b) 0.16cos( ) xt =-p
(c) 0.16sin( ) xt = p +p (d) 0.16sin( ) xt = - p +p
Q.17 Two masses m
1
 and m
2
 are suspended together by a massless
spring of constant k. When the masses are in equilibrium,
m
1
 is removed without disturbing the system. The amplitude
of oscillations is
(a) 
1
mg
k
(b)
2
mg
k
(c) 
12
() + m mg
k
1
m
2
m
(d)
12
() - m mg
k
Q.18 The composition of two simple harmonic motions of equal
periods at right angle to each other and with a phase
difference of p results in the displacement of the particle
along
(a) Straight line (b) Circle
(c) Ellipse (d) Figure of 8
Q.19A particle with restoring force proportional to
displacement and resisting force proportional to velocity
is subjected to a force F sin wt. If the amplitude of the
particle is maximum for w = w
1
 and the energy of the particle
is maximum for w = w
2
, then (where w
0 
natural frequency
of oscillation of particle)
(a)
10
w =w and 
20
w ¹w (b)
10
w =w and 
20
w =w
(c)
10
w ¹w and 
20
w =w (d)
10
w ¹w and 
20
w ¹w
Q.20 Amplitude of a wave is represented by 
c
A
a bc
=
+-
Then resonance will occur when
(a) b = – c/2 (b) b = 0 & a =  c
(c) b = – a/2 (d) None
DIRECTIONS (Q.21-Q.23) : In the following questions,
more than one of the answers  given are correct. Select the
correct answers and mark it according to the following
codes:
Codes :
(a) 1, 2 and 3 are correct (b) 1 and 2 are correct
(c) 2 and 4 are correct (d) 1 and 3 are correct
Q.21Two blocks A and B each of mass m are connected by a
massless spring of natural length L and spring constant k.
The blocks are initially resting on a smooth horizontal floor
with the spring at its natural length. A third identical block
C also of mass m moves on the floor with a speed v along
the line joining A and B and collides with A. Then
(1) The kinetic energy of the A – B system at maximum
compression of the spring is mv
2
/4
(2) The maximum compression of the spring is v m / 2k
(3) The kinetic energy of the A-B system at maximum
compression of the spring is zero
(4) The maximum compression of the spring is v m/k
Q.22A simple pendulum of length L and mass (bob) M is
oscillating in a plane about a vertical line between angular
limits – f and + f. For an angular displacement ( ) ?? , <f
the tension in the string and the velocity of the bob are T
and v respectively . The following relations hold good under
the above conditions
(1)
2
Mv
T Mgcos?
L
-=
(2) Tcos? Mg =
(3)   The magnitude of the tangential acceleration of the bob
T
a gsin? =
(4) T = Mg cos q
4
DPP/ P 28
Q.23 Identify wrong statements among the following
(1) The greater the mass of a pendulum bob, the shorter
is its frequency of oscillation
(2) A simple pendulum with a bob of mass M swings with
an angular amplitude of 40°. When its angular
amplitude is 20°, the tension in the string is less than
Mgcos20°.
(3) The fractional change in the time period of a pendulum
on changing the temperature is independent of the
length of the pendulum.
(4) As the length of a simple pendulum is increased, the
maximum velocity of its bob during its oscillation will
also decreases.
DIRECTIONS (Q.24-Q.25) : Read the passage given below
and answer the questions that follows :
A particle performs linear SHM such that it is placed on plat-
form & platform along with particles oscillate vertically up and
down with amplitude A = 1cm. If the particle does not loose
contact with platform anywhere and mass of particle is 1 kg,
find :
Q.24 The minimum, possible time period (Take g p= )
(a) 0.1 sec. (b) 0.2 sec.
(c) 0.3 sec. (d) 0.4 sec.
Q.25For minimum time period condition average potential
energy between t = 0 to t = 0.05 sec (Take g = 10 m/s
2
)
(a) 0.025 Joule (b) 0.1 Joule
(c) 0.08 Joule (d) 0.06 Joule
DIRECTIONS (Q.26-Q.28) : Each of these questions contains
two statements: Statement-1 (Assertion) and Statement-2
(Reason). Each of these questions has four alternative choices,
only one of which is the correct answer. You have to select the
correct choice.
(a) Statement-1 is True, Statement-2 is True; Statement-2 is a
correct explanation for  Statement-1.
(b) Statement-1 is True, Statement-2 is True; Statement-2 is
NOT a correct explanation for Statement-1.
(c) Statement -1 is False, Statement-2 is True.
(d) Statement -1 is True, Statement-2 is False.
Q.26 Statement-1 : Consider motion for a mass spring system
under gravity , motion of M is not a simple harmonic motion
unless Mg is negligibly small.
Statement-2 : For simple harmonic
motion acceleration must be
proportional to displacement and is
directed towards the mean position.
k = force constant
M = Mass
X
Ma = kx + Mg
Q.27 Statement-1 : The periodic time of a hard spring is less as
compared to that of a soft spring.
Statement-2 : The periodic time depends upon the spring
constant, and spring constant is large for hard spring.
Q.28Statement-1 : The percentage change in time period is
1.5%, if the length of simple pendulum increases by 3%
Statement-2:Time period is directly proportional to length of
pendulum.