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Class 11
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Physics
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Oscillations
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Hard Questions
Oscillations
Physics
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A small block is connected to one end of a massless spring of unstretched length 4.9 m. The other end of the spring (see the figure) is fixed. The system lies on a horizontal frictionless surface. The block is stretched by 0.2 m and released from rest at t=0. lt then executes simple harmonic motion with angular frequency
$ω=3π rad/s$
.
Simultaneously at t=0, a small pebble is projected with speed v from point P at an angle of 45 as shown in the figure. Point P is at a horizontal distance of 10 m from O. If the pebble hits the block at t = 1 s, the value of v is
(take
$g=10m/s_{2}$
)
A
$50 m/s$
B
$51 m/s$
C
$52 m/s$
D
$53 m/s$
Hard
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In the above question, the velocity of the rear 2 kg block after it separates from the spring will be :
A
0 m/s
B
5 m/s
C
10 m/s
D
7.5 m/s
Hard
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>
A mass
$m$
is undergoing SHM in the vertical direction about the mean position
$y_{0}$
with amplitude A and angular frequency
$ω$
. At a distance
$y$
from the mean position, the mass detaches from the spring. Assume that the spring contracts and does not obstruct the motion of
$m$
. Find the distance
$y_{∗}$
(measured from the mean position) such that the height
$h$
attained by the block is maximum.
$(Aω)_{2}>g$
A
$ω_{2}g $
B
$ω_{2}2g $
C
$2ω_{2}g $
D
None of these
Hard
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If a positively charged pendulum is oscillating in a uniform electric field as shown in Figure. Its
time period of SHM as compared to that when it was uncharged.
A
Will increase
B
Will decrease
C
Will not change
D
Will first increase then decrease
Hard
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A particle of mass m moves due to a conservative force with potential energy V(x) =
$x_{2}+a_{2}Cx $
, where C and a are positive constants.
The position(s) of stable equilibrium is/are given as
A
$x=+a$
only
B
$x=−a$
only
C
$x=−2a $
and
$+2a $
D
$x=−a$
and
$+a$
Hard
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A particle of mass m moves under a conservative force with potential energy.
$V(x)=a_{2}+x_{2} ,Cx $
where
$C$
and
$a$
are positive constants.
If the practicle starts from a point with velocity
$v$
, the range of values of
$v$
for which it escapes to -
$∞$
are given by
A
v
$<maC $
B
v
$>maC $
C
v
$>ma2C $
D
v
$<ma2C $
Hard
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>
A mass of 0.2kg is attached to the lower end of a massless spring of force-constant 200 N/m, the upper
end of which is fixed to a rigid support. Which of the following statements is/are true?
A
In equilibrium, the spring will be stretched by 1cm.
B
If the mass is raised till the spring is unstretched state and then released, it will go down by 2cm
before moving upwards.
C
The frequency of oscillation will be nearly 5 Hz
D
If the system is taken to the moon, the frequency of oscillation will be the same as on the earth.
Hard
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>
The displacement of a body executing SHM is given by x = A sin (2
$πt$
+
$3π $
). The first time from t = 0 when the velocity is maximum is:
A
0.33 sec
B
0.16 sec
C
0.25 sec
D
0.5 sec
Hard
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A particle of mass 200 g executes linear simple harmonic motion with an amplitude 10 cm. When the particles at a point midway between the mean and the extreme position, its kinetic energy is
$3π_{2}×10_{−3}J$
. Assuming the initial phase to be
$32π $
, the equation of motion of the particle will be :
A
y=10 sin
$(2πt+32π )$
cm
B
y=10 sin
$(4πt+32π )$
cm
C
y=10 cos
$(2πt+6π )$
cm
D
y=10 cos
$(2πt+3π )$
cm
Hard
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The angular frequency of a spring block system is
$ω_{0}$
This system is suspended from the ceiling of anelevator moving downwards with a constant speed v
$_{0}$
. The block is at rest relative to the elevator. Lift issuddenly stopped. Assuming the downwards as a positive direction, choose the wrong statement:
A
The amplitude of the block is
$ω_{0}v_{0} $
B
The initial phase of the block is
$π$
C
The equation of motion for the block is
$ω_{0}v_{0} sinω_{0}$
t.
D
The maximum speed of the block is v
$_{0}$
.
Hard
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>