Oscillations Practice Questions - DPP for JEE

 Page 1


PART-I (Single Correct MCQs)
1. A uniform pole of length  l = 2 L is laid
on smooth horizontal table as shown in
figure. The mass of pole is M and it is
connected to a frictionless axis at O.A
spring with force
constant k is connected to the other end. The pole
is displaced by a small angle ?
0 
from equilibrium position and released
such that it performs small oscillations. Then
(a)
(b)
(c)
Page 2


PART-I (Single Correct MCQs)
1. A uniform pole of length  l = 2 L is laid
on smooth horizontal table as shown in
figure. The mass of pole is M and it is
connected to a frictionless axis at O.A
spring with force
constant k is connected to the other end. The pole
is displaced by a small angle ?
0 
from equilibrium position and released
such that it performs small oscillations. Then
(a)
(b)
(c)
(d)
2. If a simple pendulum of length l has maximum angular displacement ?,
then the maximum K.E. of bob of mass m is
(a)
(b) mg / 2l
(c) mgl (1 – cos ?)
(d) mgl sin ?/2
3. In S.H.M., the ratio of kinetic energy at mean position to the potential
energy when the displacement is half of the amplitude is
(a)
(b)
(c)
(d)
4. Two springs, of force constants k
1
 and k
2
 are connected to a mass m as
shown. The frequency of oscillation of the mass is f. If both k
1
 and k
2
are made four times their original values, the frequency of oscillation
becomes
(a) 2 f
(b) f /2
(c) f /4
(d) 4 f
5. The bob of a simple pendulum executes simple harmonic motion in
water with a period t, while the period of oscillation of the bob is t
0
 in
air. Neglecting frictional force of water and given that the density of the
Page 3


PART-I (Single Correct MCQs)
1. A uniform pole of length  l = 2 L is laid
on smooth horizontal table as shown in
figure. The mass of pole is M and it is
connected to a frictionless axis at O.A
spring with force
constant k is connected to the other end. The pole
is displaced by a small angle ?
0 
from equilibrium position and released
such that it performs small oscillations. Then
(a)
(b)
(c)
(d)
2. If a simple pendulum of length l has maximum angular displacement ?,
then the maximum K.E. of bob of mass m is
(a)
(b) mg / 2l
(c) mgl (1 – cos ?)
(d) mgl sin ?/2
3. In S.H.M., the ratio of kinetic energy at mean position to the potential
energy when the displacement is half of the amplitude is
(a)
(b)
(c)
(d)
4. Two springs, of force constants k
1
 and k
2
 are connected to a mass m as
shown. The frequency of oscillation of the mass is f. If both k
1
 and k
2
are made four times their original values, the frequency of oscillation
becomes
(a) 2 f
(b) f /2
(c) f /4
(d) 4 f
5. The bob of a simple pendulum executes simple harmonic motion in
water with a period t, while the period of oscillation of the bob is t
0
 in
air. Neglecting frictional force of water and given that the density of the
bob is (4/3) × 1000 kg/m
3
. The relationship between t and t
0
 is
(a) t = 2t
0
(b) t = t
0
/2
(c) t = t
0
(d) t = 4t
0
6. For a simple pendulum, a graph is plotted between its kinetic energy
(KE) and potential energy (PE) against its displacement d. Which one
of the following represents these correctly? (graphs are schematic and
not drawn to scale)
(a)
(b)
(c)
(d)
7. A coin is placed on a horizontal platform which undergoes vertical
simple harmonic motion of angular frequency ?. The amplitude of
oscillation is gradually increased. The coin will leave contact with the
platform for the first time
(a) at the mean position of the platform
(b) for an amplitude of 
Page 4


PART-I (Single Correct MCQs)
1. A uniform pole of length  l = 2 L is laid
on smooth horizontal table as shown in
figure. The mass of pole is M and it is
connected to a frictionless axis at O.A
spring with force
constant k is connected to the other end. The pole
is displaced by a small angle ?
0 
from equilibrium position and released
such that it performs small oscillations. Then
(a)
(b)
(c)
(d)
2. If a simple pendulum of length l has maximum angular displacement ?,
then the maximum K.E. of bob of mass m is
(a)
(b) mg / 2l
(c) mgl (1 – cos ?)
(d) mgl sin ?/2
3. In S.H.M., the ratio of kinetic energy at mean position to the potential
energy when the displacement is half of the amplitude is
(a)
(b)
(c)
(d)
4. Two springs, of force constants k
1
 and k
2
 are connected to a mass m as
shown. The frequency of oscillation of the mass is f. If both k
1
 and k
2
are made four times their original values, the frequency of oscillation
becomes
(a) 2 f
(b) f /2
(c) f /4
(d) 4 f
5. The bob of a simple pendulum executes simple harmonic motion in
water with a period t, while the period of oscillation of the bob is t
0
 in
air. Neglecting frictional force of water and given that the density of the
bob is (4/3) × 1000 kg/m
3
. The relationship between t and t
0
 is
(a) t = 2t
0
(b) t = t
0
/2
(c) t = t
0
(d) t = 4t
0
6. For a simple pendulum, a graph is plotted between its kinetic energy
(KE) and potential energy (PE) against its displacement d. Which one
of the following represents these correctly? (graphs are schematic and
not drawn to scale)
(a)
(b)
(c)
(d)
7. A coin is placed on a horizontal platform which undergoes vertical
simple harmonic motion of angular frequency ?. The amplitude of
oscillation is gradually increased. The coin will leave contact with the
platform for the first time
(a) at the mean position of the platform
(b) for an amplitude of 
(c) for an amplitude of 
(d) at the highest position of the platform
8. A pendulum made of a uniform wire of cross sectional areaA has time
period T. When an additional mass M is added to its bob, the time
period changes to T
M
. If the Young’s modulus of the material of the
wire is Y then  is equal to:
(g = gravitational acceleration)
(a)
(b)
(c)
(d)
9. In the figure shown, the spring is light and has a force
constant k. The pulley is light and smooth and the string is
light. The suspended block has a mass m. On giving a
slight displacement vartically to the block in the
downward direction from its equilibrium position the
block executes S.H.M. on being released with time period
T. Then
(a)
(b)
(c)
Page 5


PART-I (Single Correct MCQs)
1. A uniform pole of length  l = 2 L is laid
on smooth horizontal table as shown in
figure. The mass of pole is M and it is
connected to a frictionless axis at O.A
spring with force
constant k is connected to the other end. The pole
is displaced by a small angle ?
0 
from equilibrium position and released
such that it performs small oscillations. Then
(a)
(b)
(c)
(d)
2. If a simple pendulum of length l has maximum angular displacement ?,
then the maximum K.E. of bob of mass m is
(a)
(b) mg / 2l
(c) mgl (1 – cos ?)
(d) mgl sin ?/2
3. In S.H.M., the ratio of kinetic energy at mean position to the potential
energy when the displacement is half of the amplitude is
(a)
(b)
(c)
(d)
4. Two springs, of force constants k
1
 and k
2
 are connected to a mass m as
shown. The frequency of oscillation of the mass is f. If both k
1
 and k
2
are made four times their original values, the frequency of oscillation
becomes
(a) 2 f
(b) f /2
(c) f /4
(d) 4 f
5. The bob of a simple pendulum executes simple harmonic motion in
water with a period t, while the period of oscillation of the bob is t
0
 in
air. Neglecting frictional force of water and given that the density of the
bob is (4/3) × 1000 kg/m
3
. The relationship between t and t
0
 is
(a) t = 2t
0
(b) t = t
0
/2
(c) t = t
0
(d) t = 4t
0
6. For a simple pendulum, a graph is plotted between its kinetic energy
(KE) and potential energy (PE) against its displacement d. Which one
of the following represents these correctly? (graphs are schematic and
not drawn to scale)
(a)
(b)
(c)
(d)
7. A coin is placed on a horizontal platform which undergoes vertical
simple harmonic motion of angular frequency ?. The amplitude of
oscillation is gradually increased. The coin will leave contact with the
platform for the first time
(a) at the mean position of the platform
(b) for an amplitude of 
(c) for an amplitude of 
(d) at the highest position of the platform
8. A pendulum made of a uniform wire of cross sectional areaA has time
period T. When an additional mass M is added to its bob, the time
period changes to T
M
. If the Young’s modulus of the material of the
wire is Y then  is equal to:
(g = gravitational acceleration)
(a)
(b)
(c)
(d)
9. In the figure shown, the spring is light and has a force
constant k. The pulley is light and smooth and the string is
light. The suspended block has a mass m. On giving a
slight displacement vartically to the block in the
downward direction from its equilibrium position the
block executes S.H.M. on being released with time period
T. Then
(a)
(b)
(c)
(d)
10. A point particle of mass 0.1 kg is executing S.H.M. of amplitude 0.1 m.
When the particle passes through the mean position, its kinetic energy is
8 × 10
–3
 joule. Obtain the equation of motion of this particle, if the
initial phase of oscillation is 45º.
(a)
(b)
(c)
(d)
11. A rod of length l is in motion such that its ends A and B are moving
along x-axis and y-axis respectively. It is given that  rad/sec
always. P is a fixed point on the rod. Let M be the projection of P on x-
axis. For the time interval in which ? changes from 0 to , the correct
statement is
(a) The acceleration of M is always directed towards right
(b) M executes SHM
(c) M moves with constant speed
(d) M moves with constant acceleration
12. A 1 kg mass is attached to a spring of force constant  600 N/m and rests
on a smooth
horizontal surface with other end of the spring tied to wall as shown in figure.
A second mass of 0.5 kg slides along the surface towards the first at
3m/s. If the masses make a perfectly inelastic collision, then find
amplitude and time period of oscillation of combined mass.